tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it./opt/truss2d/src/solver.cpp
1 #include "truss2d/solver.hpp"
2
3 #include <cstddef>
4 #include <stdexcept>
5 #include <vector>
6
7 #include "truss2d/dense_matrix.hpp"
8 #include "truss2d/types.hpp"
9
10 namespace truss2d {
11
12 // ============================================================================
13 // TODO(candidate): Implement the static solver for the cable/strut/bar network
14 // described in instruction.md.
15 //
16 // The four member functions below are stubs that currently return zero-valued
17 // results, so the analysis is physically wrong and the test suite FAILS.
18 // Replace the stub bodies with correct implementations. Do NOT change the
19 // public signatures declared in include/truss2d/solver.hpp, and reuse the
20 // existing support layer (DenseMatrix, solve_spd, and the Model helpers
21 // element_length / element_direction).
22 //
23 // Read instruction.md for the governing model, output conventions, and
24 // sign/units conventions. This file is the ONLY file you need to edit.
25 // ============================================================================
26
27 DenseMatrix StaticSolver::element_stiffness_global(std::size_t e) const {
28 // TODO(candidate): single-member elastic 4x4 stiffness in the global frame.
29 (void)e;
30 return DenseMatrix(4, 4); // all zeros -> wrong
31 }
32
33 DenseMatrix StaticSolver::assemble_system(const std::vector<bool>& active) const {
34 // TODO(candidate): assemble active-member elastic stiffness + spring terms.
35 (void)active;
36 const std::size_t n = model_.num_dofs();
37 return DenseMatrix(n, n); // all zeros -> wrong
38 }
39
40 std::vector<double>
41 StaticSolver::prestrain_force(const std::vector<bool>& active) const {
42 // TODO(candidate): nodal force from member prestrain for this active set.
43 (void)active;
44 const std::size_t n = model_.num_dofs();
45 return std::vector<double>(n, 0.0); // all zeros -> wrong
46 }
47
48 SolveResult StaticSolver::solve() const {
49 // TODO(candidate): validate, resolve the active set, solve, recover
50 // displacements / reactions / axial forces / active flags.
51 const std::size_t n = model_.num_dofs();
52 const std::size_t ne = model_.num_elements();
53 SolveResult result;
54 result.displacements.assign(n, 0.0);
55 result.reactions.assign(n, 0.0);
56 result.axial_forces.assign(ne, 0.0);
57 result.utilization.assign(ne, 0.0);
58 result.active.assign(ne, true);
59 return result; // trivially zero -> wrong
60 }
61
62 } // namespace truss2d
63
/opt/truss2d/include/truss2d/solver.hpp
1 #ifndef TRUSS2D_SOLVER_HPP
2 #define TRUSS2D_SOLVER_HPP
3
4 #include <cstddef>
5 #include <vector>
6
7 #include "truss2d/dense_matrix.hpp"
8 #include "truss2d/model.hpp"
9
10 namespace truss2d {
11
12 /// Result of a static analysis of a cable/strut/bar network.
13 struct SolveResult {
14 /// Nodal displacements, length == model.num_dofs(), ordered by global DOF
15 /// (2*node + component).
16 std::vector<double> displacements;
17
18 /// Support reaction forces at every global DOF, length == model.num_dofs().
19 /// Non-zero only at DOFs of nodes carrying a spring support.
20 std::vector<double> reactions;
21
22 /// Internal axial force per element, length == model.num_elements().
23 /// Sign convention: positive = tension, negative = compression. A member
24 /// that has dropped out of the load path (a slack cable / a separated
25 /// strut) reports exactly 0.
26 std::vector<double> axial_forces;
27
28 /// Signed utilization per element, length == model.num_elements(). Inactive
29 /// unilateral members report 0.
30 std::vector<double> utilization;
31
32 /// Whether each member participates in the converged load path, length ==
33 /// model.num_elements(). A Bar is always active; a Cable is inactive when
34 /// slack; a Strut is inactive when separated.
35 std::vector<bool> active;
36 };
37
38 /// Static solver for a 2D network of two-force members (bars, cables, struts)
39 /// on spring supports, with member prestrain.
40 ///
41 /// The headline departures from a classical linear pin-jointed truss are
42 /// documented in the analysis contract (instruction.md); this header only
43 /// fixes the public surface. The helpers below expose the ordinary elastic
44 /// pieces used by callers and tests.
45 class StaticSolver {
46 public:
47 explicit StaticSolver(const Model& model) : model_(model) {}
48
49 /// Run the full analysis. Calls Model::validate() first and propagates any
50 /// exception it throws. Throws std::runtime_error if the governing system
51 /// is singular (e.g. a mechanism / under-supported network).
52 SolveResult solve() const;
53
54 /// The 4x4 single-member elastic stiffness contribution for element `e`
55 /// expressed in the global frame, local DOF order {n1.x, n1.y, n2.x, n2.y}.
56 /// This is the elastic part only (it does NOT encode kind, prestrain, or
57 /// supports). Exposed for testing/reuse.
58 DenseMatrix element_stiffness_global(std::size_t e) const;
59
60 /// Assemble the full governing stiffness matrix (num_dofs x num_dofs) for a
61 /// GIVEN set of participating members `active` (length num_elements()):
62 /// the sum of the elastic stiffness of every active member plus every
63 /// spring-support contribution. Inactive members contribute nothing.
64 /// Exposed so the equilibrium residual can be checked directly.
65 DenseMatrix assemble_system(const std::vector<bool>& active) const;
66
67 /// The global nodal force vector (length num_dofs()) produced by member
68 /// prestrain for a GIVEN active set, i.e. the prestrain contribution to the
69 /// right-hand side of the governing system. Inactive members contribute
70 /// nothing. Exposed so the equilibrium residual can be checked directly.
71 std::vector<double> prestrain_force(const std::vector<bool>& active) const;
72
73 private:
74 const Model& model_;
75 };
76
77 } // namespace truss2d
78
79 #endif // TRUSS2D_SOLVER_HPP
80
/opt/truss2d/include/truss2d/model.hpp
1 #ifndef TRUSS2D_MODEL_HPP
2 #define TRUSS2D_MODEL_HPP
3
4 #include <cstddef>
5 #include <vector>
6
7 #include "truss2d/types.hpp"
8
9 namespace truss2d {
10
11 /// A 2D structural network of two-force members with spring (skew-roller)
12 /// supports and per-member tension/compression character and prestrain.
13 ///
14 /// The model is a plain data container plus light validation / derived-quantity
15 /// helpers. It is fully implemented; the numerical analysis lives in
16 /// StaticSolver (see solver.hpp).
17 class Model {
18 public:
19 std::size_t add_node(double x, double y);
20
21 /// Add a member between two existing nodes.
22 /// `kind` - Bar (default), Cable, or Strut (see types.hpp).
23 /// `prestrain` - mechanical installed axial strain (default 0).
24 /// `alpha,dT` - optional thermal expansion data (defaults 0).
25 /// Throws std::out_of_range if a node index is invalid.
26 std::size_t add_element(std::size_t n1, std::size_t n2, Section section,
27 MemberKind kind = MemberKind::Bar,
28 double prestrain = 0.0,
29 double alpha = 0.0,
30 double dT = 0.0);
31
32 /// Add a grounded spring support at `node` resisting displacement along
33 /// direction (dx, dy) with stiffness `kappa` [N/m]. The direction is
34 /// normalized internally. Throws std::out_of_range if `node` is invalid,
35 /// std::runtime_error if (dx, dy) is the zero vector or kappa <= 0.
36 /// `settlement` (optional, default 0) prescribes the spring's grounded-end
37 /// offset along (dx, dy); the spring force depends on the node displacement
38 /// along that direction RELATIVE to this offset.
39 void add_spring(std::size_t node, double dx, double dy, double kappa,
40 double settlement = 0.0);
41
42 /// Apply a force `value` [N] to a single global DOF (2*node + component).
43 /// Throws std::out_of_range if the DOF is invalid.
44 void add_load(std::size_t dof, double value);
45
46 const std::vector<Node>& nodes() const { return nodes_; }
47 const std::vector<Element>& elements() const { return elements_; }
48 const std::vector<SpringSupport>& springs() const { return springs_; }
49 const std::vector<Load>& loads() const { return loads_; }
50
51 std::size_t num_nodes() const { return nodes_.size(); }
52 std::size_t num_elements() const { return elements_.size(); }
53 std::size_t num_dofs() const { return 2 * nodes_.size(); }
54
55 /// Undeformed length of element `e` [m].
56 /// Throws std::out_of_range if `e` is invalid.
57 double element_length(std::size_t e) const;
58
59 /// Direction cosines (cos, sin) of element `e` measured from node n1
60 /// toward node n2, in the global frame.
61 /// Throws std::out_of_range if `e` is invalid, std::runtime_error if the
62 /// element has zero length.
63 Vec2 element_direction(std::size_t e) const;
64
65 /// Throws std::runtime_error if the model is structurally ill-formed
66 /// (no nodes, no elements, a zero-length element, a member with
67 /// non-positive E or A, or no spring supports at all).
68 void validate() const;
69
70 private:
71 std::vector<Node> nodes_;
72 std::vector<Element> elements_;
73 std::vector<SpringSupport> springs_;
74 std::vector<Load> loads_;
75 };
76
77 } // namespace truss2d
78
79 #endif // TRUSS2D_MODEL_HPP
80
/opt/truss2d/include/truss2d/types.hpp
1 #ifndef TRUSS2D_TYPES_HPP
2 #define TRUSS2D_TYPES_HPP
3
4 #include <array>
5 #include <cstddef>
6
7 namespace truss2d {
8
9 /// A point / vector in the 2D plane.
10 struct Vec2 {
11 double x{0.0};
12 double y{0.0};
13 };
14
15 /// A structural node with a planar position. Each node owns two
16 /// translational degrees of freedom (DOFs): x then y.
17 struct Node {
18 Vec2 position{};
19 };
20
21 /// Linear-elastic axial material + section properties for a bar element.
22 /// `E` is Young's modulus [Pa], `A` is the cross-sectional area [m^2].
23 struct Section {
24 double E{0.0};
25 double A{0.0};
26 };
27
28 /// Force-transmission character of a member.
29 ///
30 /// Bar - a two-force member that resists BOTH tension and compression
31 /// (the classical bidirectional pin-jointed bar).
32 /// Cable - a slack-capable member that resists tension ONLY; it carries no
33 /// force and contributes no stiffness when it would otherwise be in
34 /// compression.
35 /// Strut - a contact-only member that resists compression ONLY; it carries
36 /// no force and contributes no stiffness when it would otherwise be
37 /// in tension (the ends separate).
38 enum class MemberKind { Bar, Cable, Strut };
39
40 /// A two-force member connecting node `n1` to node `n2`. Indices reference the
41 /// node array stored on the Model.
42 ///
43 /// `prestrain`, `alpha`, and `dT` describe installed strain sources. They
44 /// produce internal axial force even at zero nodal displacement; see the task
45 /// contract for the sign convention.
46 struct Element {
47 std::size_t n1{0};
48 std::size_t n2{0};
49 Section section{};
50 MemberKind kind{MemberKind::Bar};
51 double prestrain{0.0};
52 double alpha{0.0};
53 double dT{0.0};
54 };
55
56 /// A grounded linear spring support at a single node.
57 ///
58 /// The support resists displacement of node `node` ALONG the unit direction
59 /// `dir` with stiffness `kappa` [N/m]. It produces no resistance to motion
60 /// perpendicular to `dir` (a skew roller). Two springs on one node with
61 /// independent directions therefore behave like a 2D elastic support; a single
62 /// spring behaves like an inclined (skew) roller.
63 ///
64 /// The support may also SETTLE: its grounded end is held at a prescribed offset
65 /// `settlement` [m] measured along `dir`, so the spring's stored elongation is
66 /// the node's displacement along `dir` relative to that offset. With
67 /// `settlement = 0` this is an ordinary grounded spring.
68 ///
69 /// `dir` is stored normalized by the Model.
70 struct SpringSupport {
71 std::size_t node{0};
72 Vec2 dir{1.0, 0.0};
73 double kappa{0.0};
74 double settlement{0.0};
75 };
76
77 /// An applied nodal force. `dof` is the global DOF index
78 /// (2*node + component) and `value` is the force magnitude [N].
79 struct Load {
80 std::size_t dof{0};
81 double value{0.0};
82 };
83
84 /// The two global DOF indices owned by a node: {2*node, 2*node + 1}.
85 inline std::array<std::size_t, 2> node_dofs(std::size_t node) {
86 return {2 * node, 2 * node + 1};
87 }
88
89 } // namespace truss2d
90
91 #endif // TRUSS2D_TYPES_HPP
92
/opt/truss2d/include/truss2d/dense_matrix.hpp
1 #ifndef TRUSS2D_DENSE_MATRIX_HPP
2 #define TRUSS2D_DENSE_MATRIX_HPP
3
4 #include <cstddef>
5 #include <stdexcept>
6 #include <vector>
7
8 namespace truss2d {
9
10 /// A small, row-major dense matrix of doubles.
11 ///
12 /// This is part of the engine's linear-algebra support layer and is fully
13 /// implemented. The truss solver uses it to hold the global stiffness matrix
14 /// and to perform the linear solve via `solve_spd`.
15 class DenseMatrix {
16 public:
17 DenseMatrix() = default;
18
19 DenseMatrix(std::size_t rows, std::size_t cols)
20 : rows_(rows), cols_(cols), data_(rows * cols, 0.0) {}
21
22 std::size_t rows() const { return rows_; }
23 std::size_t cols() const { return cols_; }
24
25 double& operator()(std::size_t r, std::size_t c) {
26 return data_[r * cols_ + c];
27 }
28 double operator()(std::size_t r, std::size_t c) const {
29 return data_[r * cols_ + c];
30 }
31
32 void fill(double v) {
33 for (auto& x : data_) x = v;
34 }
35
36 private:
37 std::size_t rows_{0};
38 std::size_t cols_{0};
39 std::vector<double> data_;
40 };
41
42 /// Solve A x = b for a symmetric positive-definite matrix A using an
43 /// LDL^T (Cholesky-style) factorization with no pivoting.
44 ///
45 /// `A` is the n-by-n system matrix and `b` is the right-hand side of length n.
46 /// Returns the solution vector x of length n.
47 ///
48 /// Throws std::runtime_error if A is not square, if the dimensions are
49 /// inconsistent, or if A is detected to be singular / not positive-definite
50 /// (a zero or negative pivot is encountered). This factorization is
51 /// numerically suitable for the reduced stiffness matrix of a properly
52 /// constrained truss, which is SPD.
53 std::vector<double> solve_spd(const DenseMatrix& A, const std::vector<double>& b);
54
55 } // namespace truss2d
56
57 #endif // TRUSS2D_DENSE_MATRIX_HPP
58
/opt/truss2d/src/model.cpp
1 #include "truss2d/model.hpp"
2
3 #include <cmath>
4 #include <stdexcept>
5
6 namespace truss2d {
7
8 std::size_t Model::add_node(double x, double y) {
9 nodes_.push_back(Node{Vec2{x, y}});
10 return nodes_.size() - 1;
11 }
12
13 std::size_t Model::add_element(std::size_t n1, std::size_t n2, Section section,
14 MemberKind kind, double prestrain,
15 double alpha, double dT) {
16 if (n1 >= nodes_.size() || n2 >= nodes_.size()) {
17 throw std::out_of_range("Model::add_element: node index out of range");
18 }
19 elements_.push_back(Element{n1, n2, section, kind, prestrain, alpha, dT});
20 return elements_.size() - 1;
21 }
22
23 void Model::add_spring(std::size_t node, double dx, double dy, double kappa,
24 double settlement) {
25 if (node >= nodes_.size()) {
26 throw std::out_of_range("Model::add_spring: node index out of range");
27 }
28 const double len = std::sqrt(dx * dx + dy * dy);
29 if (len <= 0.0) {
30 throw std::runtime_error("Model::add_spring: zero direction vector");
31 }
32 if (kappa <= 0.0) {
33 throw std::runtime_error("Model::add_spring: non-positive stiffness");
34 }
35 springs_.push_back(
36 SpringSupport{node, Vec2{dx / len, dy / len}, kappa, settlement});
37 }
38
39 void Model::add_load(std::size_t dof, double value) {
40 if (dof >= num_dofs()) {
41 throw std::out_of_range("Model::add_load: DOF out of range");
42 }
43 loads_.push_back(Load{dof, value});
44 }
45
46 double Model::element_length(std::size_t e) const {
47 if (e >= elements_.size()) {
48 throw std::out_of_range("Model::element_length: element index out of range");
49 }
50 const Element& el = elements_[e];
51 const Vec2& a = nodes_[el.n1].position;
52 const Vec2& b = nodes_[el.n2].position;
53 const double dx = b.x - a.x;
54 const double dy = b.y - a.y;
55 return std::sqrt(dx * dx + dy * dy);
56 }
57
58 Vec2 Model::element_direction(std::size_t e) const {
59 if (e >= elements_.size()) {
60 throw std::out_of_range("Model::element_direction: element index out of range");
61 }
62 const Element& el = elements_[e];
63 const Vec2& a = nodes_[el.n1].position;
64 const Vec2& b = nodes_[el.n2].position;
65 const double dx = b.x - a.x;
66 const double dy = b.y - a.y;
67 const double len = std::sqrt(dx * dx + dy * dy);
68 if (len <= 0.0) {
69 throw std::runtime_error("Model::element_direction: zero-length element");
70 }
71 return Vec2{dx / len, dy / len};
72 }
73
74 void Model::validate() const {
75 if (nodes_.empty()) {
76 throw std::runtime_error("Model::validate: model has no nodes");
77 }
78 if (elements_.empty()) {
79 throw std::runtime_error("Model::validate: model has no elements");
80 }
81 for (std::size_t e = 0; e < elements_.size(); ++e) {
82 const Element& el = elements_[e];
83 if (el.section.E <= 0.0 || el.section.A <= 0.0) {
84 throw std::runtime_error("Model::validate: element has non-positive E or A");
85 }
86 if (element_length(e) <= 0.0) {
87 throw std::runtime_error("Model::validate: element has zero length");
88 }
89 }
90 // Without at least one spring support the network is free to drift; full
91 // mechanism detection is left to the linear solve, which reports a singular
92 // system.
93 if (springs_.empty()) {
94 throw std::runtime_error(
95 "Model::validate: no spring supports (rigid-body motion not suppressed)");
96 }
97 }
98
99 } // namespace truss2d
100
List project tree and check instruction
ls -R /opt/truss2d --ignore=build 2>/dev/null | head -80; echo "---INSTRUCTION---"; cat /opt/truss2d/instruction.md 2>/dev/null | head -5
/opt/truss2d: CMakeLists.txt examples include src tests /opt/truss2d/examples: two_bar.truss /opt/truss2d/include: truss2d /opt/truss2d/include/truss2d: dense_matrix.hpp io.hpp model.hpp solver.hpp types.hpp /opt/truss2d/src: dense_matrix.cpp io.cpp main.cpp model.cpp solver.cpp /opt/truss2d/tests: CMakeLists.txt test_smoke.cpp test_util.hpp ---INSTRUCTION--- [stdout] /opt/truss2d: CMakeLists.txt examples include src tests /opt/truss2d/examples: two_bar.truss /opt/truss2d/include: truss2d /opt/truss2d/include/truss2d: dense_matrix.hpp io.hpp model.hpp solver.hpp types.hpp /opt/truss2d/src: dense_matrix.cpp io.cpp main.cpp model.cpp solver.cpp /opt/truss2d/tests: CMakeLists.txt test_smoke.cpp test_util.hpp ---INSTRUCTION---
/opt/truss2d/tests/test_smoke.cpp
1 // Trivial smoke test for the truss2d engine.
2 //
3 // This checks only that the engine links and that the data model + result
4 // shapes are self-consistent. It deliberately makes NO numerical-correctness
5 // assertions, so it passes against the shipped stub solver. The real
6 // correctness / invariant / discriminator suite is provided separately by the
7 // grader.
8
9 #include <cstddef>
10 #include <sstream>
11
12 #include "truss2d/io.hpp"
13 #include "truss2d/model.hpp"
14 #include "truss2d/solver.hpp"
15 #include "test_util.hpp"
16
17 using truss2d::Model;
18 using truss2d::Section;
19 using truss2d::MemberKind;
20 using truss2d::SolveResult;
21 using truss2d::StaticSolver;
22
23 TRUSS2D_TEST("model_construction_shapes") {
24 Model m;
25 m.add_node(0.0, 0.0);
26 m.add_node(2.0, 0.0);
27 m.add_element(0, 1, Section{2.0e11, 1.0e-3}, MemberKind::Bar, 0.0);
28 m.add_spring(0, 1.0, 0.0, 1.0e13);
29 m.add_spring(0, 0.0, 1.0, 1.0e13);
30 m.add_spring(1, 0.0, 1.0, 1.0e13);
31 m.add_load(2, 1.0e3);
32
33 truss2d_test::expect(m.num_nodes() == 2, "two nodes");
34 truss2d_test::expect(m.num_dofs() == 4, "four DOFs");
35 truss2d_test::expect(m.num_elements() == 1, "one element");
36 truss2d_test::expect(m.springs().size() == 3, "three springs");
37 }
38
39 TRUSS2D_TEST("result_vectors_have_expected_lengths") {
40 Model m;
41 m.add_node(0.0, 0.0);
42 m.add_node(3.0, 0.0);
43 m.add_node(3.0, 4.0);
44 m.add_element(0, 1, Section{2.0e11, 1.0e-3});
45 m.add_element(1, 2, Section{2.0e11, 1.0e-3});
46 m.add_element(0, 2, Section{2.0e11, 1.0e-3});
47 m.add_spring(0, 1.0, 0.0, 1.0e13);
48 m.add_spring(0, 0.0, 1.0, 1.0e13);
49 m.add_spring(1, 0.0, 1.0, 1.0e13);
50
51 SolveResult r = StaticSolver(m).solve();
52 truss2d_test::expect(r.displacements.size() == m.num_dofs(),
53 "displacements length == num_dofs");
54 truss2d_test::expect(r.reactions.size() == m.num_dofs(),
55 "reactions length == num_dofs");
56 truss2d_test::expect(r.axial_forces.size() == m.num_elements(),
57 "axial_forces length == num_elements");
58 truss2d_test::expect(r.utilization.size() == m.num_elements(),
59 "utilization length == num_elements");
60 truss2d_test::expect(r.active.size() == m.num_elements(),
61 "active length == num_elements");
62 }
63
64 TRUSS2D_TEST("parser_reads_records") {
65 const char* text =
66 "node 0 0\n"
67 "node 2 0\n"
68 "elem 0 1 2.0e11 1.0e-3 1 -5.0e-4 1.2e-5 -25\n"
69 "spring 0 1 0 1.0e13\n"
70 "spring 0 0 1 1.0e13\n"
71 "spring 1 0 1 1.0e13\n"
72 "load 1 1 -1.0e3\n";
73 std::istringstream in(text);
74 Model m = truss2d::parse_model(in);
75 truss2d_test::expect(m.num_nodes() == 2, "parsed two nodes");
76 truss2d_test::expect(m.num_elements() == 1, "parsed one element");
77 truss2d_test::expect(m.elements()[0].kind == MemberKind::Cable,
78 "parsed cable kind");
79 truss2d_test::expect_near(m.elements()[0].alpha, 1.2e-5, 1e-15,
80 "parsed alpha");
81 truss2d_test::expect_near(m.elements()[0].dT, -25.0, 1e-15,
82 "parsed dT");
83 truss2d_test::expect(m.springs().size() == 3, "parsed three springs");
84 }
85
86 TRUSS2D_TEST_MAIN()
87
/opt/truss2d/tests/test_util.hpp
1 #ifndef TRUSS2D_TEST_UTIL_HPP
2 #define TRUSS2D_TEST_UTIL_HPP
3
4 // Minimal dependency-free test harness for the truss2d suite.
5 //
6 // Each test executable defines test functions and registers them with
7 // TRUSS2D_TEST(name) { ... }. main() (provided by test_main.hpp via
8 // TRUSS2D_TEST_MAIN) runs every registered test and returns non-zero if any
9 // assertion fails, which CTest interprets as a failure.
10
11 #include <cmath>
12 #include <cstddef>
13 #include <functional>
14 #include <iostream>
15 #include <string>
16 #include <vector>
17
18 namespace truss2d_test {
19
20 struct Case {
21 std::string name;
22 std::function<void()> fn;
23 };
24
25 inline std::vector<Case>& registry() {
26 static std::vector<Case> cases;
27 return cases;
28 }
29
30 struct Registrar {
31 Registrar(const std::string& name, std::function<void()> fn) {
32 registry().push_back(Case{name, std::move(fn)});
33 }
34 };
35
36 // Thrown by an assertion failure to abort the current test case.
37 struct AssertionError {
38 std::string message;
39 };
40
41 inline void expect(bool cond, const std::string& what) {
42 if (!cond) {
43 throw AssertionError{what};
44 }
45 }
46
47 inline void expect_near(double got, double want, double tol, const std::string& what) {
48 if (std::fabs(got - want) > tol) {
49 throw AssertionError{what + " (got " + std::to_string(got) +
50 ", want " + std::to_string(want) +
51 ", tol " + std::to_string(tol) + ")"};
52 }
53 }
54
55 inline int run_all() {
56 int failures = 0;
57 for (const auto& c : registry()) {
58 try {
59 c.fn();
60 std::cout << "[ PASS ] " << c.name << "\n";
61 } catch (const AssertionError& e) {
62 std::cout << "[ FAIL ] " << c.name << ": " << e.message << "\n";
63 ++failures;
64 } catch (const std::exception& e) {
65 std::cout << "[ FAIL ] " << c.name
66 << ": unexpected exception: " << e.what() << "\n";
67 ++failures;
68 } catch (...) {
69 std::cout << "[ FAIL ] " << c.name << ": unknown exception\n";
70 ++failures;
71 }
72 }
73 std::cout << "----\n"
74 << (registry().size() - failures) << "/" << registry().size()
75 << " tests passed\n";
76 return failures == 0 ? 0 : 1;
77 }
78
79 } // namespace truss2d_test
80
81 #define TRUSS2D_CONCAT_INNER(a, b) a##b
82 #define TRUSS2D_CONCAT(a, b) TRUSS2D_CONCAT_INNER(a, b)
83
84 #define TRUSS2D_TEST(NAME) \
85 static void TRUSS2D_CONCAT(truss2d_test_fn_, __LINE__)(); \
86 static ::truss2d_test::Registrar TRUSS2D_CONCAT(truss2d_test_reg_, \
87 __LINE__){ \
88 NAME, &TRUSS2D_CONCAT(truss2d_test_fn_, __LINE__)}; \
89 static void TRUSS2D_CONCAT(truss2d_test_fn_, __LINE__)()
90
91 #define TRUSS2D_TEST_MAIN() \
92 int main() { return ::truss2d_test::run_all(); }
93
94 #endif // TRUSS2D_TEST_UTIL_HPP
95
/opt/truss2d/src/dense_matrix.cpp
1 #include "truss2d/dense_matrix.hpp"
2
3 #include <cmath>
4
5 namespace truss2d {
6
7 std::vector<double> solve_spd(const DenseMatrix& A, const std::vector<double>& b) {
8 const std::size_t n = A.rows();
9 if (A.cols() != n) {
10 throw std::runtime_error("solve_spd: matrix is not square");
11 }
12 if (b.size() != n) {
13 throw std::runtime_error("solve_spd: right-hand side size mismatch");
14 }
15
16 // LDL^T factorization (no pivoting): A = L D L^T with L unit-lower
17 // triangular and D diagonal. Suitable for the SPD reduced stiffness
18 // matrix of a well-constrained truss.
19 DenseMatrix L(n, n);
20 std::vector<double> D(n, 0.0);
21
22 for (std::size_t j = 0; j < n; ++j) {
23 double dj = A(j, j);
24 for (std::size_t k = 0; k < j; ++k) {
25 dj -= L(j, k) * L(j, k) * D[k];
26 }
27 // A genuine SPD matrix has strictly positive pivots. A tiny tolerance
28 // guards against round-off while still flagging singular systems.
29 if (dj <= 1e-12) {
30 throw std::runtime_error(
31 "solve_spd: matrix is singular or not positive-definite");
32 }
33 D[j] = dj;
34 L(j, j) = 1.0;
35 for (std::size_t i = j + 1; i < n; ++i) {
36 double s = A(i, j);
37 for (std::size_t k = 0; k < j; ++k) {
38 s -= L(i, k) * L(j, k) * D[k];
39 }
40 L(i, j) = s / dj;
41 }
42 }
43
44 // Forward solve L z = b.
45 std::vector<double> z(n, 0.0);
46 for (std::size_t i = 0; i < n; ++i) {
47 double s = b[i];
48 for (std::size_t k = 0; k < i; ++k) {
49 s -= L(i, k) * z[k];
50 }
51 z[i] = s;
52 }
53
54 // Diagonal solve D y = z.
55 std::vector<double> y(n, 0.0);
56 for (std::size_t i = 0; i < n; ++i) {
57 y[i] = z[i] / D[i];
58 }
59
60 // Back solve L^T x = y.
61 std::vector<double> x(n, 0.0);
62 for (std::size_t ii = 0; ii < n; ++ii) {
63 const std::size_t i = n - 1 - ii;
64 double s = y[i];
65 for (std::size_t k = i + 1; k < n; ++k) {
66 s -= L(k, i) * x[k];
67 }
68 x[i] = s;
69 }
70
71 return x;
72 }
73
74 } // namespace truss2d
75
/opt/truss2d/src/io.cpp
1 #include "truss2d/io.hpp"
2
3 #include <fstream>
4 #include <iomanip>
5 #include <iostream>
6 #include <sstream>
7 #include <stdexcept>
8 #include <string>
9
10 namespace truss2d {
11
12 namespace {
13
14 [[noreturn]] void fail(std::size_t line_no, const std::string& msg) {
15 std::ostringstream oss;
16 oss << "parse_model: line " << line_no << ": " << msg;
17 throw std::runtime_error(oss.str());
18 }
19
20 const char* kind_name(MemberKind k) {
21 switch (k) {
22 case MemberKind::Bar: return "bar";
23 case MemberKind::Cable: return "cable";
24 case MemberKind::Strut: return "strut";
25 }
26 return "?";
27 }
28
29 } // namespace
30
31 Model parse_model(std::istream& in) {
32 Model model;
33 std::string line;
34 std::size_t line_no = 0;
35
36 while (std::getline(in, line)) {
37 ++line_no;
38 const auto hash = line.find('#');
39 if (hash != std::string::npos) {
40 line.erase(hash);
41 }
42 std::istringstream ls(line);
43 std::string tag;
44 if (!(ls >> tag)) {
45 continue; // blank / comment-only line
46 }
47
48 if (tag == "node") {
49 double x, y;
50 if (!(ls >> x >> y)) fail(line_no, "expected: node <x> <y>");
51 model.add_node(x, y);
52 } else if (tag == "elem") {
53 std::size_t n1, n2;
54 double E, A;
55 if (!(ls >> n1 >> n2 >> E >> A)) {
56 fail(line_no,
57 "expected: elem <n1> <n2> <E> <A> [kind] [prestrain] [alpha] [dT]");
58 }
59 int kind_code = 0;
60 double prestrain = 0.0;
61 double alpha = 0.0;
62 double dT = 0.0;
63 ls >> kind_code; // optional
64 ls >> prestrain; // optional
65 ls >> alpha; // optional
66 ls >> dT; // optional
67 MemberKind kind = MemberKind::Bar;
68 if (kind_code == 1) kind = MemberKind::Cable;
69 else if (kind_code == 2) kind = MemberKind::Strut;
70 else if (kind_code != 0) fail(line_no, "kind must be 0/1/2 (bar/cable/strut)");
71 try {
72 model.add_element(n1, n2, Section{E, A}, kind, prestrain, alpha, dT);
73 } catch (const std::exception& ex) {
74 fail(line_no, ex.what());
75 }
76 } else if (tag == "spring") {
77 std::size_t node;
78 double dx, dy, kappa;
79 if (!(ls >> node >> dx >> dy >> kappa)) {
80 fail(line_no, "expected: spring <node> <dx> <dy> <kappa>");
81 }
82 try {
83 model.add_spring(node, dx, dy, kappa);
84 } catch (const std::exception& ex) {
85 fail(line_no, ex.what());
86 }
87 } else if (tag == "load") {
88 std::size_t node, comp;
89 double value;
90 if (!(ls >> node >> comp >> value)) {
91 fail(line_no, "expected: load <node> <comp> <value>");
92 }
93 if (comp > 1) fail(line_no, "component must be 0 (x) or 1 (y)");
94 try {
95 model.add_load(2 * node + comp, value);
96 } catch (const std::exception& ex) {
97 fail(line_no, ex.what());
98 }
99 } else {
100 fail(line_no, "unknown record '" + tag + "'");
101 }
102 }
103
104 return model;
105 }
106
107 Model parse_model_file(const std::string& path) {
108 std::ifstream in(path);
109 if (!in) {
110 throw std::runtime_error("parse_model_file: cannot open '" + path + "'");
111 }
112 return parse_model(in);
113 }
114
115 void write_report(std::ostream& out, const Model& model, const SolveResult& result) {
116 out << std::scientific << std::setprecision(6);
117 out << "# Truss2D static analysis report\n";
118 out << "nodes=" << model.num_nodes()
119 << " elements=" << model.num_elements()
120 << " dofs=" << model.num_dofs() << "\n\n";
121
122 out << "[displacements] (node, ux, uy)\n";
123 for (std::size_t i = 0; i < model.num_nodes(); ++i) {
124 out << i << " " << result.displacements[2 * i] << " "
125 << result.displacements[2 * i + 1] << "\n";
126 }
127
128 out << "\n[reactions] (node, Rx, Ry)\n";
129 for (std::size_t i = 0; i < model.num_nodes(); ++i) {
130 out << i << " " << result.reactions[2 * i] << " "
131 << result.reactions[2 * i + 1] << "\n";
132 }
133
134 out << "\n[axial_forces] (element, kind, active, N [+tension], utilization)\n";
135 for (std::size_t e = 0; e < model.num_elements(); ++e) {
136 const bool act = e < result.active.size() ? result.active[e] : true;
137 const double util = e < result.utilization.size() ? result.utilization[e] : 0.0;
138 out << e << " " << kind_name(model.elements()[e].kind) << " "
139 << (act ? 1 : 0) << " " << result.axial_forces[e] << " "
140 << util << "\n";
141 }
142 }
143
144 } // namespace truss2d
145
#include "truss2d/solver.hpp"
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <stdexcept>
#include <vector>
#include "truss2d/dense_matrix.hpp"
#include "truss2d/types.hpp"
namespace truss2d {
namespace {
// Installed stress-free strain: mechanical lack-of-fit plus thermal, combined
// to first order. A positive value means the member's natural length exceeds
// its joint spacing (manufactured too long / heated), which is compressive when
// restrained; a negative value is tensile.
inline double installed_strain(const Element& el) {
return el.prestrain + el.alpha * el.dT;
}
} // namespace
DenseMatrix StaticSolver::element_stiffness_global(std::size_t e) const {
const Element& el = model_.elements().at(e);
const double L0 = model_.element_length(e);
const Vec2 d = model_.element_direction(e);
const double k = el.section.E * el.section.A / L0;
const double c = d.x;
const double s = d.y;
// dd^T block, with the [[B, -B], [-B, B]] global layout.
const double B[2][2] = {{c * c, c * s}, {c * s, s * s}};
DenseMatrix Ke(4, 4);
for (int a = 0; a < 2; ++a) {
for (int b = 0; b < 2; ++b) {
const double v = k * B[a][b];
Ke(a, b) += v;
Ke(a, b + 2) -= v;
Ke(a + 2, b) -= v;
Ke(a + 2, b + 2) += v;
}
}
return Ke;
}
DenseMatrix StaticSolver::assemble_system(const std::vector<bool>& active) const {
const std::size_t n = model_.num_dofs();
DenseMatrix K(n, n);
const auto& elems = model_.elements();
// Ordinary elastic stiffness of participating members.
for (std::size_t e = 0; e < elems.size(); ++e) {
if (e < active.size() && !active[e]) continue;
const DenseMatrix Ke = element_stiffness_global(e);
const std::size_t g[4] = {2 * elems[e].n1, 2 * elems[e].n1 + 1,
2 * elems[e].n2, 2 * elems[e].n2 + 1};
for (int a = 0; a < 4; ++a) {
for (int b = 0; b < 4; ++b) {
K(g[a], g[b]) += Ke(a, b);
}
}
}
// Spring supports: kappa * d d^T at the supported node's block. Always
// present (a support is not gated by the member active set).
for (const auto& sp : model_.springs()) {
const std::size_t bx = 2 * sp.node;
const std::size_t by = 2 * sp.node + 1;
const double dx = sp.dir.x;
const double dy = sp.dir.y;
K(bx, bx) += sp.kappa * dx * dx;
K(bx, by) += sp.kappa * dx * dy;
K(by, bx) += sp.kappa * dy * dx;
K(by, by) += sp.kappa * dy * dy;
}
return K;
}
std::vector<double>
StaticSolver::prestrain_force(const std::vector<bool>& active) const {
const std::size_t n = model_.num_dofs();
std::vector<double> F(n, 0.0);
const auto& elems = model_.elements();
for (std::size_t e = 0; e < elems.size(); ++e) {
if (e < active.size() && !active[e]) continue;
const Element& el = elems[e];
const double eps0 = installed_strain(el);
if (eps0 == 0.0) continue;
// Installed axial force is N0 = -p at zero displacement; the equivalent
// nodal load that reproduces it is F_n1 = -p d, F_n2 = +p d.
const double p = el.section.E * el.section.A * eps0;
const Vec2 d = model_.element_direction(e);
F[2 * el.n1] -= p * d.x;
F[2 * el.n1 + 1] -= p * d.y;
F[2 * el.n2] += p * d.x;
F[2 * el.n2 + 1] += p * d.y;
}
return F;
}
SolveResult StaticSolver::solve() const {
model_.validate();
const std::size_t n = model_.num_dofs();
const auto& elems = model_.elements();
const std::size_t ne = elems.size();
// Per-element cached quantities.
std::vector<double> L0(ne), kax(ne), p_install(ne);
std::vector<Vec2> dir(ne);
for (std::size_t e = 0; e < ne; ++e) {
L0[e] = model_.element_length(e);
dir[e] = model_.element_direction(e);
const double EA = elems[e].section.E * elems[e].section.A;
kax[e] = EA / L0[e];
p_install[e] = EA * installed_strain(elems[e]);
}
// Right-hand-side contributions that do not depend on the active set.
std::vector<double> F_applied(n, 0.0);
for (const auto& ld : model_.loads()) F_applied[ld.dof] += ld.value;
std::vector<double> F_settle(n, 0.0);
for (const auto& sp : model_.springs()) {
// Settlement RHS term kappa * settlement * d (the prescribed offset of
// the spring's grounded end loads the structure).
const double f = sp.kappa * sp.settlement;
F_settle[2 * sp.node] += f * sp.dir.x;
F_settle[2 * sp.node + 1] += f * sp.dir.y;
}
// Recover the elastic axial force of every member from a displacement field
// (no geometric term; the initial-stress effect does not change N).
auto recover = [&](const std::vector<double>& u) {
std::vector<double> N(ne, 0.0);
for (std::size_t e = 0; e < ne; ++e) {
const std::size_t a = elems[e].n1;
const std::size_t b = elems[e].n2;
const double dux = u[2 * b] - u[2 * a];
const double duy = u[2 * b + 1] - u[2 * a + 1];
const double delta = dux * dir[e].x + duy * dir[e].y;
N[e] = kax[e] * delta - p_install[e];
}
return N;
};
std::vector<bool> active(ne, true);
// Seed member forces with the installed prestress so a taut prestressed
// member contributes transverse (initial-stress) stiffness from the very
// first solve, keeping otherwise transversely-soft cable nets well posed.
std::vector<double> N(ne);
for (std::size_t e = 0; e < ne; ++e) N[e] = -p_install[e];
std::vector<double> u(n, 0.0);
const int max_outer = static_cast<int>(2 * ne) + 20;
const int max_geo = 500;
for (int outer = 0; outer < max_outer; ++outer) {
// Inner Picard iteration: find the member forces, displacements they
// produce, and forces recovered from those displacements that coincide.
for (int gi = 0; gi < max_geo; ++gi) {
DenseMatrix K = assemble_system(active);
// Add the force-dependent transverse (initial-stress) stiffness of
// each participating member: (N/L0) * [[P,-P],[-P,P]] with the
// transverse projection P = I - d d^T.
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) continue;
const double g = N[e] / L0[e];
if (g == 0.0) continue;
const double c = dir[e].x;
const double s = dir[e].y;
const double P[2][2] = {{s * s, -c * s}, {-c * s, c * c}};
const std::size_t gd[4] = {2 * elems[e].n1, 2 * elems[e].n1 + 1,
2 * elems[e].n2, 2 * elems[e].n2 + 1};
for (int a = 0; a < 2; ++a) {
for (int b = 0; b < 2; ++b) {
const double v = g * P[a][b];
K(gd[a], gd[b]) += v;
K(gd[a], gd[b + 2]) -= v;
K(gd[a + 2], gd[b]) -= v;
K(gd[a + 2], gd[b + 2]) += v;
}
}
}
std::vector<double> F = F_applied;
const std::vector<double> Fp = prestrain_force(active);
for (std::size_t i = 0; i < n; ++i) F[i] += Fp[i] + F_settle[i];
const std::vector<double> u_new = solve_spd(K, F);
const std::vector<double> N_new = recover(u_new);
double diff = 0.0, scale = 0.0;
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) continue;
diff = std::max(diff, std::fabs(N_new[e] - N[e]));
scale = std::max(scale, std::fabs(N_new[e]));
}
u = u_new;
for (std::size_t e = 0; e < ne; ++e) {
if (active[e]) N[e] = N_new[e];
}
if (diff <= 1e-12 * scale + 1e-14) break;
}
// Resolve the active set from the consistent displacement field. A
// cable/strut is judged by its total axial force (installed strain plus
// elastic extension), recovered even when currently inactive.
const std::vector<double> N_all = recover(u);
bool changed = false;
for (std::size_t e = 0; e < ne; ++e) {
bool desired = true;
switch (elems[e].kind) {
case MemberKind::Bar:
desired = true;
break;
case MemberKind::Cable:
desired = (N_all[e] > 0.0); // tension-only
break;
case MemberKind::Strut:
desired = (N_all[e] < 0.0); // compression-only
break;
}
if (desired != active[e]) {
active[e] = desired;
changed = true;
}
}
if (!changed) break;
}
const std::vector<double> N_all = recover(u);
SolveResult result;
result.displacements = u;
result.reactions.assign(n, 0.0);
result.axial_forces.assign(ne, 0.0);
result.utilization.assign(ne, 0.0);
result.active.assign(ne, false);
const double sigma_allow = 2.5e8;
for (std::size_t e = 0; e < ne; ++e) {
result.active[e] = active[e];
if (active[e]) {
const double Ne = N_all[e];
result.axial_forces[e] = Ne;
const double capacity = sigma_allow * elems[e].section.A;
result.utilization[e] = Ne / capacity;
}
// Dropped unilateral members report exactly zero force / utilization.
}
// Support reactions: force applied by each spring to the structure, which
// opposes its stored extension (node displacement along the direction minus
// the prescribed settlement offset).
for (const auto& sp : model_.springs()) {
const double along =
u[2 * sp.node] * sp.dir.x + u[2 * sp.node + 1] * sp.dir.y;
const double force = -sp.kappa * (along - sp.settlement);
result.reactions[2 * sp.node] += force * sp.dir.x;
result.reactions[2 * sp.node + 1] += force * sp.dir.y;
}
return result;
}
} // namespace truss2d
Configure, build, run tests
cmake -S . -B build -DCMAKE_BUILD_TYPE=Release >/tmp/cm.log 2>&1 && cmake --build build --parallel >/tmp/build.log 2>&1 && echo BUILD_OK && cd build && ctest --output-on-failure 2>&1 | tail -20 || (echo "FAILED"; tail -30 /tmp/build.log)
BUILD_OK
Test project /opt/truss2d/build
Start 1: smoke
1/1 Test #1: smoke ............................ Passed 0.00 sec
100% tests passed, 0 tests failed out of 1
Total Test time (real) = 0.00 sec
[stdout]
BUILD_OK
Test project /opt/truss2d/build
Start 1: smoke
1/1 Test #1: smoke ............................ Passed 0.00 sec
100% tests passed, 0 tests failed out of 1
Total Test time (real) = 0.00 sec#include <cmath>
#include <cstdio>
#include <vector>
#include "truss2d/model.hpp"
#include "truss2d/solver.hpp"
#include "truss2d/dense_matrix.hpp"
using namespace truss2d;
static int failures = 0;
static void chk(bool c, const char* what, double got = 0, double want = 0) {
if (!c) { printf(" FAIL: %s (got %.6g want %.6g)\n", what, got, want); ++failures; }
else printf(" ok: %s\n", what);
}
static void near(double got, double want, double tol, const char* what) {
chk(std::fabs(got - want) <= tol * (1 + std::fabs(want)), what, got, want);
}
// Check global equilibrium residual: K(active)*u - (Fapplied+Fprestrain+Fsettle)
// should be balanced by geometric forces + reactions. Simpler: check that each
// free node is in equilibrium under member axial forces + applied + reactions +
// geometric transverse forces. We instead verify equilibrium directly.
static void check_equilibrium(const Model& m, const SolveResult& r, const char* tag) {
const std::size_t n = m.num_dofs();
std::vector<double> resid(n, 0.0);
// applied loads
for (const auto& ld : m.loads()) resid[ld.dof] += ld.value;
// reactions
for (std::size_t i = 0; i < n; ++i) resid[i] += r.reactions[i];
// member internal forces (axial + geometric transverse)
const auto& els = m.elements();
for (std::size_t e = 0; e < els.size(); ++e) {
if (!r.active[e]) continue;
const double L0 = m.element_length(e);
const Vec2 d = m.element_direction(e);
const std::size_t a = els[e].n1, b = els[e].n2;
const double N = r.axial_forces[e];
// axial: member pulls n1 toward n2 (+d) in tension
resid[2*a] += N * d.x; resid[2*a+1] += N * d.y;
resid[2*b] -= N * d.x; resid[2*b+1] -= N * d.y;
// geometric transverse force = (N/L0) P (u_rel)
const double c = d.x, s = d.y;
const double ux = r.displacements[2*b] - r.displacements[2*a];
const double uy = r.displacements[2*b+1] - r.displacements[2*a+1];
const double Px = s*s*ux - c*s*uy;
const double Py = -c*s*ux + c*c*uy;
const double g = N / L0;
// force on n1 from geometric = +g*P*u_rel ; on n2 = -g*P*u_rel
resid[2*a] += g*Px; resid[2*a+1] += g*Py;
resid[2*b] -= g*Px; resid[2*b+1] -= g*Py;
}
double mx = 0; for (double v : resid) mx = std::max(mx, std::fabs(v));
printf(" [%s] max equilibrium residual = %.3e\n", tag, mx);
chk(mx < 1e-3, "equilibrium balanced", mx, 0);
}
int main() {
const double E = 2.0e11, A = 1.0e-3, k = E*A;
// ---- Case 1: single horizontal bar, node1 loaded +x, springs hold both ----
printf("Case 1: axial bar\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A});
// node0 fully fixed via two strong springs, node1 y fixed
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,0,1,1e16);
m.add_load(2, 1.0e4); // +x at node1
SolveResult r = StaticSolver(m).solve();
// u1x = F*L/(EA) = 1e4*2/(2e8)=1e-4
near(r.displacements[2], 1e4*2.0/k, 1e-9, "u1x");
near(r.axial_forces[0], 1.0e4, 1e-3, "axial = +1e4 (tension)");
near(r.reactions[0], -1.0e4, 1e-2, "reaction node0 x = -1e4");
check_equilibrium(m, r, "case1");
}
// ---- Case 2: prestrain too-long bar (compression when restrained) ----
printf("Case 2: prestrain\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A}, MemberKind::Bar, 1e-3); // too long
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,1,0,1e16); m.add_spring(1,0,1,1e16);
SolveResult r = StaticSolver(m).solve();
// fully restrained: N = -EA*eps0 = -2e8*1e-3 = -2e5 (compression)
near(r.axial_forces[0], -k*1e-3, 1e-3, "prestrain N = -EA*eps0 (compression)");
check_equilibrium(m, r, "case2");
}
// ---- Case 3: thermal heating bar restrained -> compression ----
printf("Case 3: thermal\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A}, MemberKind::Bar, 0.0, 1.2e-5, 50.0);
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,1,0,1e16); m.add_spring(1,0,1,1e16);
SolveResult r = StaticSolver(m).solve();
near(r.axial_forces[0], -k*1.2e-5*50.0, 1e-3, "thermal heating -> compression");
check_equilibrium(m, r, "case3");
}
// ---- Case 4: cable goes slack under compression load ----
printf("Case 4: cable slack\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A}, MemberKind::Cable);
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,0,1,1e16); m.add_spring(1,1,0,1e6); // soft x at node1
m.add_load(2, -1.0e3); // push node1 toward node0 -> compression -> slack
SolveResult r = StaticSolver(m).solve();
chk(!r.active[0], "cable inactive (slack)");
near(r.axial_forces[0], 0.0, 1e-12, "slack cable zero force");
near(r.utilization[0], 0.0, 1e-12, "slack cable zero util");
check_equilibrium(m, r, "case4");
}
// ---- Case 5: cable taut under tension load ----
printf("Case 5: cable taut\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A}, MemberKind::Cable);
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,0,1,1e16);
m.add_load(2, 1.0e4);
SolveResult r = StaticSolver(m).solve();
chk(r.active[0], "cable active (taut)");
near(r.axial_forces[0], 1.0e4, 1e-3, "taut cable N=1e4");
near(r.utilization[0], 1.0e4/(2.5e8*A), 1e-9, "util = N/(sigma*A)");
check_equilibrium(m, r, "case5");
}
// ---- Case 6: settlement of a spring loads structure ----
printf("Case 6: settlement\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A});
// node0 fixed, node1 x has spring with settlement
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,0,1,1e16);
double kap = 1e7, s0 = 1e-3;
m.add_spring(1,1,0,kap,s0); // settle node1 in +x by s0 (relative)
SolveResult r = StaticSolver(m).solve();
// node1 x: bar stiffness kbar=EA/L=1e8 in series-ish with spring kap.
// Equilibrium at node1x: kbar*u1 + kap*(u1 - s0) = 0 -> u1 = kap*s0/(kbar+kap)
double kbar = k/2.0;
double u1 = kap*s0/(kbar+kap);
near(r.displacements[2], u1, 1e-9, "settlement u1x");
// reaction at node1x = -kap*(u1 - s0)
near(r.reactions[2], -kap*(u1 - s0), 1e-3, "settlement reaction");
check_equilibrium(m, r, "case6");
}
// ---- Case 7: initial-stress transverse stiffness (taut cable + lateral) ----
printf("Case 7: prestressed cable transverse\n");
{
// Two collinear cables along x, mid node loaded in -y; transverse
// stiffness comes from pretension (geometric). Pretension via prestrain.
Model m;
m.add_node(-1.0,0); m.add_node(0,0); m.add_node(1.0,0);
// cables pretensioned (manufactured short -> tension): prestrain<0
double pre = -1e-3;
m.add_element(0,1, Section{E,A}, MemberKind::Cable, pre);
m.add_element(1,2, Section{E,A}, MemberKind::Cable, pre);
// anchor ends fully, mid node free in y, x lightly sprung
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(2,1,0,1e16); m.add_spring(2,0,1,1e16);
m.add_spring(1,1,0,1e16); // mid node x restrained
m.add_load(3, -100.0); // small lateral load at mid node y
SolveResult r = StaticSolver(m).solve();
chk(r.active[0] && r.active[1], "both cables taut");
printf(" mid uy=%.6e N0=%.6e N1=%.6e\n",
r.displacements[3], r.axial_forces[0], r.axial_forces[1]);
// Pretension T ~ EA*1e-3 = 2e5. Transverse stiffness ~ 2*T/L (two cables)
// small-disp: F = (T/L0_0 + T/L0_1)*uy*... here both unit length.
// Approx linearized: 2*(T)*uy/L = F -> uy = -F*L/(2T) with T~2e5
check_equilibrium(m, r, "case7");
chk(r.displacements[3] < 0, "mid deflects downward");
}
// ---- Case 8: strut separates under tension ----
printf("Case 8: strut separation\n");
{
Model m;
m.add_node(0,0); m.add_node(2.0,0);
m.add_element(0,1, Section{E,A}, MemberKind::Strut);
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,0,1,1e16); m.add_spring(1,1,0,1e6);
m.add_load(2, 1.0e3); // pull apart -> tension -> strut separates
SolveResult r = StaticSolver(m).solve();
chk(!r.active[0], "strut inactive (separated)");
near(r.axial_forces[0], 0.0, 1e-12, "separated strut zero force");
check_equilibrium(m, r, "case8");
}
// ---- Case 9: classic 2-bar truss, compare to hand calc ----
printf("Case 9: two-bar truss\n");
{
// node0(0,0), node1(3,0), node2(3,4). bars 0-2 and 1-2. Load at node2.
Model m;
m.add_node(0,0); m.add_node(3,0); m.add_node(3,4);
m.add_element(0,2, Section{E,A}); // diagonal length 5
m.add_element(1,2, Section{E,A}); // vertical length 4
m.add_spring(0,1,0,1e16); m.add_spring(0,0,1,1e16);
m.add_spring(1,1,0,1e16); m.add_spring(1,0,1,1e16);
m.add_load(5, -1.0e4); // -y at node2
SolveResult r = StaticSolver(m).solve();
check_equilibrium(m, r, "case9");
printf(" N_diag=%.4e N_vert=%.4e\n", r.axial_forces[0], r.axial_forces[1]);
}
printf("\n%s (%d failures)\n", failures? "FAILURES" : "ALL PASS", failures);
return failures ? 1 : 0;
}
Compile and run verification harness
cd /opt/truss2d && g++ -std=c++17 -O2 -Iinclude tests/verify.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/verify 2>&1 | head -20 && /tmp/verify
Case 1: axial bar
ok: u1x
ok: axial = +1e4 (tension)
ok: reaction node0 x = -1e4
[case1] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 2: prestrain
ok: prestrain N = -EA*eps0 (compression)
[case2] max equilibrium residual = 2.910e-11
ok: equilibrium balanced
Case 3: thermal
ok: thermal heating -> compression
[case3] max equilibrium residual = 1.455e-11
ok: equilibrium balanced
Case 4: cable slack
ok: cable inactive (slack)
ok: slack cable zero force
ok: slack cable zero util
[case4] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 5: cable taut
ok: cable active (taut)
ok: taut cable N=1e4
ok: util = N/(sigma*A)
[case5] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 6: settlement
ok: settlement u1x
ok: settlement reaction
[case6] max equilibrium residual = 1.819e-12
ok: equilibrium balanced
Case 7: prestressed cable transverse
ok: both cables taut
mid uy=-2.500000e-04 N0=2.000000e+05 N1=2.000000e+05
[case7] max equilibrium residual = 1.421e-14
ok: equilibrium balanced
ok: mid deflects downward
Case 8: strut separation
ok: strut inactive (separated)
ok: separated strut zero force
[case8] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 9: two-bar truss
[case9] max equilibrium residual = 2.612e-12
ok: equilibrium balanced
N_diag=1.1114e+00 N_vert=-1.0001e+04
ALL PASS (0 failures)
[stdout]
Case 1: axial bar
ok: u1x
ok: axial = +1e4 (tension)
ok: reaction node0 x = -1e4
[case1] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 2: prestrain
ok: prestrain N = -EA*eps0 (compression)
[case2] max equilibrium residual = 2.910e-11
ok: equilibrium balanced
Case 3: thermal
ok: thermal heating -> compression
[case3] max equilibrium residual = 1.455e-11
ok: equilibrium balanced
Case 4: cable slack
ok: cable inactive (slack)
ok: slack cable zero force
ok: slack cable zero util
[case4] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 5: cable taut
ok: cable active (taut)
ok: taut cable N=1e4
ok: util = N/(sigma*A)
[case5] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 6: settlement
ok: settlement u1x
ok: settlement reaction
[case6] max equilibrium residual = 1.819e-12
ok: equilibrium balanced
Case 7: prestressed cable transverse
ok: both cables taut
mid uy=-2.500000e-04 N0=2.000000e+05 N1=2.000000e+05
[case7] max equilibrium residual = 1.421e-14
ok: equilibrium balanced
ok: mid deflects downward
Case 8: strut separation
ok: strut inactive (separated)
ok: separated strut zero force
[case8] max equilibrium residual = 0.000e+00
ok: equilibrium balanced
Case 9: two-bar truss
[case9] max equilibrium residual = 2.612e-12
ok: equilibrium balanced
N_diag=1.1114e+00 N_vert=-1.0001e+04
ALL PASS (0 failures)Clean up temp test, rebuild, run ctest
rm -f tests/verify.cpp && cmake --build build --parallel >/tmp/b.log 2>&1 && cd build && ctest --output-on-failure 2>&1 | tail -5
1/1 Test #1: smoke ............................ Passed 0.00 sec 100% tests passed, 0 tests failed out of 1 Total Test time (real) = 0.00 sec [stdout] 1/1 Test #1: smoke ............................ Passed 0.00 sec 100% tests passed, 0 tests failed out of 1 Total Test time (real) = 0.00 sec
No file changes, the agent left the workspace untouched.
== Restoring pristine project ==
== Staging candidate solver ==
== Injecting hidden grading tests ==
== Configuring (cmake) ==
-- The CXX compiler identification is GNU 11.4.0
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Check for working CXX compiler: /usr/bin/c++ - skipped
-- Detecting CXX compile features
-- Detecting CXX compile features - done
-- Configuring done
-- Generating done
-- Build files have been written to: /tmp/tmp.kCcUtoMh5L/truss2d/build_grade
== Building ==
[ 5%] Building CXX object CMakeFiles/truss2d.dir/src/io.cpp.o
[ 10%] Building CXX object CMakeFiles/truss2d.dir/src/dense_matrix.cpp.o
[ 15%] Building CXX object CMakeFiles/truss2d.dir/src/model.cpp.o
[ 21%] Building CXX object CMakeFiles/truss2d.dir/src/solver.cpp.o
[ 26%] Linking CXX static library libtruss2d.a
[ 26%] Built target truss2d
[ 31%] Building CXX object tests/CMakeFiles/test_core.dir/test_core.cpp.o
[ 36%] Building CXX object CMakeFiles/truss2d_cli.dir/src/main.cpp.o
[ 42%] Building CXX object tests/CMakeFiles/test_soak.dir/test_soak.cpp.o
[ 47%] Building CXX object tests/CMakeFiles/test_unilateral.dir/test_unilateral.cpp.o
[ 52%] Building CXX object tests/CMakeFiles/test_degenerate.dir/test_degenerate.cpp.o
[ 57%] Building CXX object tests/CMakeFiles/test_geometric.dir/test_geometric.cpp.o
[ 63%] Building CXX object tests/CMakeFiles/test_settlement.dir/test_settlement.cpp.o
[ 68%] Linking CXX executable truss2d_cli
[ 68%] Built target truss2d_cli
[ 73%] Linking CXX executable test_degenerate
[ 73%] Built target test_degenerate
[ 78%] Linking CXX executable test_soak
[ 78%] Built target test_soak
[ 84%] Linking CXX executable test_unilateral
[ 89%] Linking CXX executable test_settlement
[ 89%] Built target test_unilateral
[ 89%] Built target test_settlement
[ 94%] Linking CXX executable test_core
[100%] Linking CXX executable test_geometric
[100%] Built target test_core
[100%] Built target test_geometric
== Running hidden tests ==
Test project /tmp/tmp.kCcUtoMh5L/truss2d/build_grade
Start 1: test_core
1/6 Test #1: test_core ........................ Passed 0.00 sec
Start 2: test_unilateral
2/6 Test #2: test_unilateral .................. Passed 0.00 sec
Start 3: test_geometric
3/6 Test #3: test_geometric ................... Passed 0.00 sec
Start 4: test_soak
4/6 Test #4: test_soak ........................ Passed 0.00 sec
Start 5: test_degenerate
5/6 Test #5: test_degenerate .................. Passed 0.00 sec
Start 6: test_settlement
6/6 Test #6: test_settlement .................. Passed 0.00 sec
100% tests passed, 0 tests failed out of 6
Label Time Summary:
hidden = 0.02 sec*proc (6 tests)
Total Test time (real) = 0.02 sec
PASS: all hidden tests passedReproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_b4b02fd20e2e433f. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.
Trial trial_b4b02fd20e2e433f · verifier authoritative; classifier explanatory.