tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it./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/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/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
/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/instruction.md
File does not exist. Note: your current working directory is /opt/truss2d. [error] tool reported failure
ls -R --ignore=build | head -80
.: CMakeLists.txt examples include src tests ./examples: two_bar.truss ./include: truss2d ./include/truss2d: dense_matrix.hpp io.hpp model.hpp solver.hpp types.hpp ./src: dense_matrix.cpp io.cpp main.cpp model.cpp solver.cpp ./tests: CMakeLists.txt test_smoke.cpp test_util.hpp [stdout] .: CMakeLists.txt examples include src tests ./examples: two_bar.truss ./include: truss2d ./include/truss2d: dense_matrix.hpp io.hpp model.hpp solver.hpp types.hpp ./src: dense_matrix.cpp io.cpp main.cpp model.cpp solver.cpp ./tests: CMakeLists.txt test_smoke.cpp test_util.hpp
/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/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 {
// Allowable axial stress for utilization reporting [Pa].
constexpr double kAllowableStress = 2.5e8;
// The four global DOF indices owned by element `e`, in local order
// {n1.x, n1.y, n2.x, n2.y}.
struct ElemDofs {
std::size_t d[4];
};
ElemDofs elem_dofs(const Element& el) {
return ElemDofs{{2 * el.n1, 2 * el.n1 + 1, 2 * el.n2, 2 * el.n2 + 1}};
}
// Geometric (initial-stress) 4x4 stiffness of a member carrying total axial
// force `N`, expressed in the global frame. Tension (N > 0) stiffens the
// transverse mode; compression softens it. It is N/L times the outer product
// of the transverse projection operator, so it vanishes for rigid translation
// and for relative motion along the member axis.
DenseMatrix geometric_stiffness(const Vec2& dir, double L, double N) {
const double c = dir.x;
const double s = dir.y;
// Transverse projection vector: extension transverse to the axis.
const double T[4] = {s, -c, -s, c};
const double f = N / L;
DenseMatrix Kg(4, 4);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
Kg(i, j) = f * T[i] * T[j];
}
}
return Kg;
}
} // namespace
DenseMatrix StaticSolver::element_stiffness_global(std::size_t e) const {
const Element& el = model_.elements().at(e);
const double L = model_.element_length(e);
const Vec2 dir = model_.element_direction(e);
const double c = dir.x;
const double s = dir.y;
const double k = el.section.E * el.section.A / L;
// Axial extension projection: extension = B^T u, with u in local DOF order.
const double B[4] = {-c, -s, c, s};
DenseMatrix Ke(4, 4);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
Ke(i, j) = k * B[i] * B[j];
}
}
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();
for (std::size_t e = 0; e < elems.size(); ++e) {
if (!active[e]) continue;
const DenseMatrix Ke = element_stiffness_global(e);
const ElemDofs g = elem_dofs(elems[e]);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
K(g.d[i], g.d[j]) += Ke(i, j);
}
}
}
// Grounded spring supports: each resists displacement along its unit
// direction only, contributing kappa * dir dir^T at the node's DOFs.
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 (!active[e]) continue;
const Element& el = elems[e];
const Vec2 dir = model_.element_direction(e);
const double c = dir.x;
const double s = dir.y;
// Installed (stress-free) strain: mechanical lack-of-fit plus thermal.
// A positive installed strain means the member is too long: with the
// ends held it sits in compression and pushes them apart.
const double eps0 = el.prestrain + el.alpha * el.dT;
const double EAeps = el.section.E * el.section.A * eps0;
const double B[4] = {-c, -s, c, s};
const ElemDofs g = elem_dofs(el);
for (int i = 0; i < 4; ++i) {
F[g.d[i]] += EAeps * B[i];
}
}
return F;
}
SolveResult StaticSolver::solve() const {
model_.validate();
const std::size_t n = model_.num_dofs();
const std::size_t ne = model_.num_elements();
const auto& elems = model_.elements();
// Total axial force recovered from a displacement field for element `e`:
// N = EA (extension/L - installed strain), positive in tension. This is the
// ordinary elastic recovery and does NOT include the geometric effect.
const auto recover = [&](std::size_t e, const std::vector<double>& u) {
const Element& el = elems[e];
const double L = model_.element_length(e);
const Vec2 dir = model_.element_direction(e);
const double c = dir.x;
const double s = dir.y;
const double B[4] = {-c, -s, c, s};
const ElemDofs g = elem_dofs(el);
double ext = 0.0;
for (int i = 0; i < 4; ++i) ext += B[i] * u[g.d[i]];
const double eps0 = el.prestrain + el.alpha * el.dT;
return el.section.E * el.section.A * (ext / L - eps0);
};
// Right-hand side for a given active set: prestrain forces + applied loads
// + spring settlement (a prescribed grounded-end offset stores stretch
// relative to it, so it loads the structure as +kappa*settlement*dir).
const auto build_rhs = [&](const std::vector<bool>& active) {
std::vector<double> F = prestrain_force(active);
for (const auto& ld : model_.loads()) {
F[ld.dof] += ld.value;
}
for (const auto& sp : model_.springs()) {
F[2 * sp.node] += sp.kappa * sp.settlement * sp.dir.x;
F[2 * sp.node + 1] += sp.kappa * sp.settlement * sp.dir.y;
}
return F;
};
// For a fixed active set, solve the consistent initial-stress equilibrium:
// the tangent stiffness uses the geometric contribution of the very member
// forces that the resulting displacements recover. Picard iteration on the
// member forces, starting from the purely elastic state (no geometric
// term), reaches that fixed point.
const auto solve_state = [&](const std::vector<bool>& active,
std::vector<double>& u_out,
std::vector<double>& N_out) {
const std::vector<double> F = build_rhs(active);
std::vector<double> N(ne, 0.0);
std::vector<double> u(n, 0.0);
for (int iter = 0; iter < 500; ++iter) {
DenseMatrix K = assemble_system(active);
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) continue;
const DenseMatrix Kg = geometric_stiffness(
model_.element_direction(e), model_.element_length(e), N[e]);
const ElemDofs g = elem_dofs(elems[e]);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
K(g.d[i], g.d[j]) += Kg(i, j);
}
}
}
u = solve_spd(K, F);
double max_diff = 0.0;
double max_N = 0.0;
std::vector<double> Nnew(ne, 0.0);
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) continue;
Nnew[e] = recover(e, u);
max_diff = std::max(max_diff, std::abs(Nnew[e] - N[e]));
max_N = std::max(max_N, std::abs(Nnew[e]));
}
N = Nnew;
if (max_diff <= 1e-12 * (1.0 + max_N)) break;
}
u_out = std::move(u);
N_out = std::move(N);
};
// Active-set iteration enforcing the unilateral rules: a cable carries
// tension only, a strut compression only; a bar always participates. A
// member is judged by its total axial force recovered from the current
// displacement field.
std::vector<bool> active(ne, true);
std::vector<double> u(n, 0.0);
std::vector<double> N(ne, 0.0);
const int max_outer = static_cast<int>(2 * ne) + 16;
for (int outer = 0; outer <= max_outer; ++outer) {
solve_state(active, u, N);
bool changed = false;
std::vector<bool> desired(ne, true);
for (std::size_t e = 0; e < ne; ++e) {
const Element& el = elems[e];
// Small force scale to avoid chatter at the slack/taut boundary.
const double thr = 1e-9 * el.section.E * el.section.A;
const double Npot = recover(e, u);
switch (el.kind) {
case MemberKind::Bar:
desired[e] = true;
break;
case MemberKind::Cable:
desired[e] = (Npot > thr); // tension-only
break;
case MemberKind::Strut:
desired[e] = (Npot < -thr); // compression-only
break;
}
if (desired[e] != active[e]) changed = true;
}
if (!changed) break;
active = desired;
}
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 = active;
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) continue;
const Element& el = elems[e];
result.axial_forces[e] = N[e];
result.utilization[e] = N[e] / (kAllowableStress * el.section.A);
}
// Support reactions: force the spring applies to the structure, opposing
// the spring's stretch relative to any prescribed settlement.
for (const auto& sp : model_.springs()) {
const double un =
u[2 * sp.node] * sp.dir.x + u[2 * sp.node + 1] * sp.dir.y;
const double force = -sp.kappa * (un - 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
cmake -S . -B build -DCMAKE_BUILD_TYPE=Release >/dev/null 2>&1 && cmake --build build --parallel 2>&1 | tail -20 && cd build && ctest --output-on-failure 2>&1 | tail -25
[ 11%] Building CXX object CMakeFiles/truss2d.dir/src/io.cpp.o
[ 22%] Building CXX object CMakeFiles/truss2d.dir/src/dense_matrix.cpp.o
[ 33%] Building CXX object CMakeFiles/truss2d.dir/src/model.cpp.o
[ 44%] Building CXX object CMakeFiles/truss2d.dir/src/solver.cpp.o
[ 55%] Linking CXX static library libtruss2d.a
[ 55%] Built target truss2d
[ 66%] Building CXX object tests/CMakeFiles/test_smoke.dir/test_smoke.cpp.o
[ 77%] Building CXX object CMakeFiles/truss2d_cli.dir/src/main.cpp.o
[ 88%] Linking CXX executable truss2d_cli
[ 88%] Built target truss2d_cli
[100%] Linking CXX executable test_smoke
[100%] Built target test_smoke
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]
[ 11%] Building CXX object CMakeFiles/truss2d.dir/src/io.cpp.o
[ 22%] Building CXX object CMakeFiles/truss2d.dir/src/dense_matrix.cpp.o
[ 33%] Building CXX object CMakeFiles/truss2d.dir/src/model.cpp.o
[ 44%] Building CXX object CMakeFiles/truss2d.dir/src/solver.cpp.o
[ 55%] Linking CXX static library libtruss2d.a
[ 55%] Built target truss2d
[ 66%] Building CXX object tests/CMakeFiles/test_smoke.dir/test_smoke.cpp.o
[ 77%] Building CXX object CMakeFiles/truss2d_cli.dir/src/main.cpp.o
[ 88%] Linking CXX executable truss2d_cli
[ 88%] Built target truss2d_cli
[100%] Linking CXX executable test_smoke
[100%] Built target test_smoke
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 "truss2d/model.hpp"
#include "truss2d/solver.hpp"
using namespace truss2d;
static int fails = 0;
static void chk(const char* name, double got, double exp, double tol) {
double d = std::abs(got - exp);
bool ok = d <= tol * (1 + std::abs(exp));
if (!ok) ++fails;
printf("%-40s got=%+.6e exp=%+.6e %s\n", name, got, exp, ok ? "OK" : "FAIL");
}
int main() {
const double E = 2.0e11, A = 1.0e-3;
const double STIFF = 1.0e15;
// --- Test A: single horizontal bar, tension under axial load ---
{
Model m;
m.add_node(0, 0); m.add_node(2, 0);
m.add_element(0, 1, {E, A});
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 0, 1, STIFF);
m.add_load(2, 1.0e3); // node1 x
auto r = StaticSolver(m).solve();
double k = E * A / 2.0;
chk("A bar axial force", r.axial_forces[0], 1.0e3, 1e-6);
chk("A node1 ux", r.displacements[2], 1.0e3 / k, 1e-6);
chk("A reaction node0 x", r.reactions[0], -1.0e3, 1e-5);
}
// --- Test B: prestrain too long -> compression between fixed nodes ---
{
Model m;
m.add_node(0, 0); m.add_node(2, 0);
double eps0 = 1e-4;
m.add_element(0, 1, {E, A}, MemberKind::Bar, eps0);
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 1, 0, STIFF); m.add_spring(1, 0, 1, STIFF);
auto r = StaticSolver(m).solve();
chk("B prestrain compression", r.axial_forces[0], -E * A * eps0, 1e-6);
}
// --- Test C: thermal heating -> compression between fixed nodes ---
{
Model m;
m.add_node(0, 0); m.add_node(2, 0);
double alpha = 1.2e-5, dT = 30;
m.add_element(0, 1, {E, A}, MemberKind::Bar, 0.0, alpha, dT);
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 1, 0, STIFF); m.add_spring(1, 0, 1, STIFF);
auto r = StaticSolver(m).solve();
chk("C thermal compression", r.axial_forces[0], -E * A * alpha * dT, 1e-6);
}
// --- Test D: cable goes slack under compressive load ---
{
Model m;
m.add_node(0, 0); m.add_node(2, 0);
m.add_element(0, 1, {E, A}, MemberKind::Cable);
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 0, 1, STIFF); m.add_spring(1, 1, 0, 1.0e6);
m.add_load(2, -1.0e3); // push node1 toward node0 -> compression -> slack
auto r = StaticSolver(m).solve();
chk("D cable slack force", r.axial_forces[0], 0.0, 1e-9);
printf(" D active=%d (expect 0)\n", (int)r.active[0]);
if (r.active[0]) ++fails;
// node1 resisted only by its own x spring 1e6: u = -1e3/1e6
chk("D node1 ux", r.displacements[2], -1.0e-3, 1e-6);
}
// --- Test E: cable in tension stays active ---
{
Model m;
m.add_node(0, 0); m.add_node(2, 0);
m.add_element(0, 1, {E, A}, MemberKind::Cable);
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 0, 1, STIFF);
m.add_load(2, 1.0e3);
auto r = StaticSolver(m).solve();
chk("E cable tension", r.axial_forces[0], 1.0e3, 1e-6);
if (!r.active[0]) ++fails;
}
// --- Test F: strut separates under tension load ---
{
Model m;
m.add_node(0, 0); m.add_node(2, 0);
m.add_element(0, 1, {E, A}, MemberKind::Strut);
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 0, 1, STIFF); m.add_spring(1, 1, 0, 1.0e6);
m.add_load(2, 1.0e3); // pull away -> tension -> separate
auto r = StaticSolver(m).solve();
chk("F strut separated force", r.axial_forces[0], 0.0, 1e-9);
if (r.active[0]) ++fails;
}
// --- Test G: settlement loads structure ---
{
// bar fixed at node0, node1 supported by x-spring with settlement.
Model m;
m.add_node(0, 0); m.add_node(2, 0);
m.add_element(0, 1, {E, A});
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
m.add_spring(1, 0, 1, STIFF);
double ks = 1.0e8, settle = 1.0e-4;
m.add_spring(1, 1, 0, ks, settle); // x-spring at node1 with settlement
auto r = StaticSolver(m).solve();
// node1 x: bar k=1e8 to fixed node0, spring ks=1e8 grounded at offset
// settle. Equilibrium: k*u + ks*(u - settle) = 0 -> u = ks*settle/(k+ks)
double k = E * A / 2.0;
double u1 = ks * settle / (k + ks);
chk("G settlement node1 ux", r.displacements[2], u1, 1e-6);
// bar force = k*u (tension since u>0 stretches bar)
chk("G settlement bar force", r.axial_forces[0], k * u1, 1e-6);
// reaction = -ks*(u - settle)
chk("G settlement reaction", r.reactions[2], -ks * (u1 - settle), 1e-6);
}
// --- Test H: 45-degree bar, load resolves correctly ---
{
Model m;
m.add_node(0, 0); m.add_node(3, 4); // L=5
m.add_element(0, 1, {E, A});
m.add_spring(0, 1, 0, STIFF); m.add_spring(0, 0, 1, STIFF);
// node1 supported transverse to bar so it only moves along bar axis.
// transverse dir to (0.6,0.8) is (-0.8,0.6)
m.add_spring(1, -0.8, 0.6, STIFF);
// load along bar axis at node1: F*(0.6,0.8), F=1e3
m.add_load(2, 0.6e3); m.add_load(3, 0.8e3);
auto r = StaticSolver(m).solve();
chk("H inclined bar axial", r.axial_forces[0], 1.0e3, 1e-5);
}
printf("\n%s (%d failures)\n", fails ? "FAILURES" : "ALL PASS", fails);
return fails ? 1 : 0;
}
cd /opt/truss2d && g++ -std=c++17 -Iinclude verify.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/verify 2>&1 | tail -20 && /tmp/verify
A bar axial force got=+1.000000e+03 exp=+1.000000e+03 OK A node1 ux got=+1.000000e-05 exp=+1.000000e-05 OK A reaction node0 x got=-1.000000e+03 exp=-1.000000e+03 OK B prestrain compression got=-2.000000e+04 exp=-2.000000e+04 OK C thermal compression got=-7.199999e+04 exp=-7.200000e+04 OK D cable slack force got=+0.000000e+00 exp=+0.000000e+00 OK D active=0 (expect 0) D node1 ux got=-1.000000e-03 exp=-1.000000e-03 OK E cable tension got=+1.000000e+03 exp=+1.000000e+03 OK F strut separated force got=+0.000000e+00 exp=+0.000000e+00 OK G settlement node1 ux got=+5.000000e-05 exp=+5.000000e-05 OK G settlement bar force got=+5.000000e+03 exp=+5.000000e+03 OK G settlement reaction got=+5.000000e+03 exp=+5.000000e+03 OK H inclined bar axial got=+1.000000e+03 exp=+1.000000e+03 OK ALL PASS (0 failures) [stdout] A bar axial force got=+1.000000e+03 exp=+1.000000e+03 OK A node1 ux got=+1.000000e-05 exp=+1.000000e-05 OK A reaction node0 x got=-1.000000e+03 exp=-1.000000e+03 OK B prestrain compression got=-2.000000e+04 exp=-2.000000e+04 OK C thermal compression got=-7.199999e+04 exp=-7.200000e+04 OK D cable slack force got=+0.000000e+00 exp=+0.000000e+00 OK D active=0 (expect 0) D node1 ux got=-1.000000e-03 exp=-1.000000e-03 OK E cable tension got=+1.000000e+03 exp=+1.000000e+03 OK F strut separated force got=+0.000000e+00 exp=+0.000000e+00 OK G settlement node1 ux got=+5.000000e-05 exp=+5.000000e-05 OK G settlement bar force got=+5.000000e+03 exp=+5.000000e+03 OK G settlement reaction got=+5.000000e+03 exp=+5.000000e+03 OK H inclined bar axial got=+1.000000e+03 exp=+1.000000e+03 OK ALL PASS (0 failures)
cat > /tmp/vg.cpp <<'EOF'
#include <cmath>
#include <cstdio>
#include "truss2d/model.hpp"
#include "truss2d/solver.hpp"
using namespace truss2d;
int main(){
const double E=2.0e11,A=1.0e-3,STIFF=1.0e15;
// Pretensioned horizontal member; node1 x held stiff, y free. Transverse load.
// Transverse stiffness should be N/L (geometric). Without geometric term the
// system would be singular (node1 y unconstrained).
{
Model m; m.add_node(0,0); m.add_node(2,0);
double eps0=-1e-3; // too short -> tension
m.add_element(0,1,{E,A},MemberKind::Bar,eps0);
m.add_spring(0,1,0,STIFF); m.add_spring(0,0,1,STIFF);
m.add_spring(1,1,0,STIFF); // hold node1 x
double P=100.0; m.add_load(3,P); // node1 y
auto r=StaticSolver(m).solve();
double N=r.axial_forces[0];
double uy=r.displacements[3];
double Nexp=E*A*1e-3; // ~2e5
double uy_exp=P/(N/2.0); // L=2
printf("geo tension N=%.6e (exp~%.6e) uy=%.6e exp=%.6e ratio=%.6f\n",
N,Nexp,uy,uy_exp,uy/uy_exp);
// tension: increasing pretension should decrease uy
}
// Same with compression pretension (softens). Add a small y spring so it
// stays positive-definite.
{
Model m; m.add_node(0,0); m.add_node(2,0);
double eps0=+5e-4; // too long -> compression
m.add_element(0,1,{E,A},MemberKind::Bar,eps0);
m.add_spring(0,1,0,STIFF); m.add_spring(0,0,1,STIFF);
m.add_spring(1,1,0,STIFF);
double ky=2.0e5; m.add_spring(1,0,1,ky); // y spring keeps PD
double P=100.0; m.add_load(3,P);
auto r=StaticSolver(m).solve();
double N=r.axial_forces[0]; // negative
double uy=r.displacements[3];
// transverse stiffness = ky + N/L (N negative softens)
double uy_exp=P/(ky + N/2.0);
printf("geo compr N=%.6e uy=%.6e exp=%.6e ratio=%.6f\n",N,uy,uy_exp,uy/uy_exp);
}
return 0;
}
EOF
g++ -std=c++17 -Iinclude /tmp/vg.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/vg && /tmp/vgExit code 134 terminate called after throwing an instance of 'std::runtime_error' what(): solve_spd: matrix is singular or not positive-definite /bin/bash: line 95: 1737 Aborted /tmp/vg [error] tool reported failure
/opt/truss2d/src/solver.cpp
const std::vector<double> F = build_rhs(active);
std::vector<double> N(ne, 0.0);
std::vector<double> u(n, 0.0);
for (int iter = 0; iter < 500; ++iter) { const std::vector<double> F = build_rhs(active);
std::vector<double> N(ne, 0.0);
// Seed the geometric term with the installed prestress force (the axial
// force at zero displacement). This is the dominant component and gives
// the taut transverse stiffness immediately, so a structure stabilized
// only by prestress does not start from a singular tangent.
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) continue;
const Element& el = elems[e];
N[e] = -el.section.E * el.section.A *
(el.prestrain + el.alpha * el.dT);
}
std::vector<double> u(n, 0.0);
for (int iter = 0; iter < 500; ++iter) {g++ -std=c++17 -Iinclude /tmp/vg.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/vg && /tmp/vg && echo "---rerun analytic---" && g++ -std=c++17 -Iinclude verify.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/verify && /tmp/verify | tail -3
geo tension N=2.000000e+05 (exp~2.000000e+05) uy=1.000000e-03 exp=1.000000e-03 ratio=1.000000 geo compr N=-9.999998e+04 uy=6.666666e-04 exp=6.666666e-04 ratio=1.000000 ---rerun analytic--- H inclined bar axial got=+1.000000e+03 exp=+1.000000e+03 OK ALL PASS (0 failures) [stdout] geo tension N=2.000000e+05 (exp~2.000000e+05) uy=1.000000e-03 exp=1.000000e-03 ratio=1.000000 geo compr N=-9.999998e+04 uy=6.666666e-04 exp=6.666666e-04 ratio=1.000000 ---rerun analytic--- H inclined bar axial got=+1.000000e+03 exp=+1.000000e+03 OK ALL PASS (0 failures)
cmake --build build --parallel 2>&1 | tail -2 && (cd build && ctest --output-on-failure 2>&1 | tail -4) && rm -f verify.cpp && rm -f /tmp/verify /tmp/vg /tmp/vg.cpp && echo cleaned
[ 88%] Built target test_smoke [100%] Built target truss2d_cli 100% tests passed, 0 tests failed out of 1 Total Test time (real) = 0.00 sec cleaned [stdout] [ 88%] Built target test_smoke [100%] Built target truss2d_cli 100% tests passed, 0 tests failed out of 1 Total Test time (real) = 0.00 sec cleaned
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.Xl9MNRKyg8/truss2d/build_grade
== Building ==
[ 5%] Building CXX object CMakeFiles/truss2d.dir/src/dense_matrix.cpp.o
[ 10%] Building CXX object CMakeFiles/truss2d.dir/src/io.cpp.o
[ 15%] Building CXX object CMakeFiles/truss2d.dir/src/solver.cpp.o
[ 21%] Building CXX object CMakeFiles/truss2d.dir/src/model.cpp.o
[ 26%] Linking CXX static library libtruss2d.a
[ 26%] Built target truss2d
[ 31%] Building CXX object CMakeFiles/truss2d_cli.dir/src/main.cpp.o
[ 36%] Building CXX object tests/CMakeFiles/test_core.dir/test_core.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_settlement.dir/test_settlement.cpp.o
[ 57%] Building CXX object tests/CMakeFiles/test_geometric.dir/test_geometric.cpp.o
[ 63%] Building CXX object tests/CMakeFiles/test_degenerate.dir/test_degenerate.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_settlement
[ 84%] Linking CXX executable test_soak
[ 84%] Built target test_settlement
[ 89%] Linking CXX executable test_unilateral
[ 89%] Built target test_soak
[ 89%] Built target test_unilateral
[ 94%] Linking CXX executable test_core
[ 94%] Built target test_core
[100%] Linking CXX executable test_geometric
[100%] Built target test_geometric
== Running hidden tests ==
Test project /tmp/tmp.Xl9MNRKyg8/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 0.01 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_cfad4489f13a4c89. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.
Trial trial_cfad4489f13a4c89 · verifier authoritative; classifier explanatory.