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
/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
ls -R /opt/truss2d --ignore=build 2>/dev/null | head -60; echo "---INSTRUCTION---"; cat /opt/truss2d/instruction.md 2>/dev/null | head -200
/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/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
/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
#include "truss2d/solver.hpp"
#include <array>
#include <cmath>
#include <cstddef>
#include <stdexcept>
#include <vector>
#include "truss2d/dense_matrix.hpp"
#include "truss2d/types.hpp"
namespace truss2d {
// ============================================================================
// Static solver for a planar network of two-force members (bars/cables/struts)
// on linear spring supports, with installed (mechanical + thermal) strain and
// the small-displacement initial-stress (stress-stiffening) effect.
//
// Conventions
// * Each node owns DOFs {2*node, 2*node+1} = {x, y}.
// * For an element from n1 to n2 with unit direction (c, s) and length L,
// the axial extension to first order is delta = b . u_local with
// b = {-c, -s, c, s}. The elastic axial stiffness is k = E*A/L and the
// element elastic stiffness is k * b b^T.
// * Installed free strain eps = prestrain + alpha*dT (combined to first
// order). A positive free strain means the member is manufactured/heated
// "too long" and is initially compressive. The total axial force
// (positive in tension) recovered from a displacement field is
// N = (E*A/L) * (b . u_local) - E*A*eps.
// * The prestrain nodal load (RHS) for a member is E*A*eps * b.
// * A spring at `node` along unit `dir` with stiffness kappa adds
// kappa * dir dir^T to that node's 2x2 block and, when settling, a nodal
// load kappa*settlement*dir to the RHS. Its reaction on the structure is
// -kappa*(u.dir - settlement)*dir.
// * The transverse initial-stress stiffness of an active member carrying
// total axial force N is (N/L) * g g^T with g = {s, -c, -s, c}. It
// vanishes for rigid translation and for axial relative motion, stiffens
// in tension and softens in compression, and is part of solve()'s tangent
// only (never of the elastic helper outputs).
// ============================================================================
namespace {
constexpr double kSigmaAllow = 2.5e8; // allowable stress [Pa]
inline std::array<std::size_t, 4> elem_dofs(const Element& el) {
return {2 * el.n1, 2 * el.n1 + 1, 2 * el.n2, 2 * el.n2 + 1};
}
} // 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 d = model_.element_direction(e);
const double c = d.x;
const double s = d.y;
const double k = el.section.E * el.section.A / L;
const double b[4] = {-c, -s, c, s};
DenseMatrix K(4, 4);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
K(i, j) = k * b[i] * b[j];
}
}
return K;
}
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 std::array<std::size_t, 4> dofs = elem_dofs(elems[e]);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
K(dofs[i], dofs[j]) += ke(i, j);
}
}
}
// Grounded spring supports: kappa * dir dir^T at the node's 2x2 block.
for (const SpringSupport& sp : model_.springs()) {
const std::size_t dx = 2 * sp.node;
const std::size_t dy = 2 * sp.node + 1;
const double ex = sp.dir.x;
const double ey = sp.dir.y;
K(dx, dx) += sp.kappa * ex * ex;
K(dx, dy) += sp.kappa * ex * ey;
K(dy, dx) += sp.kappa * ey * ex;
K(dy, dy) += sp.kappa * ey * ey;
}
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 d = model_.element_direction(e);
const double c = d.x;
const double s = d.y;
const double eps = el.prestrain + el.alpha * el.dT;
const double f = el.section.E * el.section.A * eps;
const double b[4] = {-c, -s, c, s};
const std::array<std::size_t, 4> dofs = elem_dofs(el);
for (int i = 0; i < 4; ++i) {
F[dofs[i]] += f * 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();
// ---- Constant external load vector: applied loads + spring settlement. ----
std::vector<double> f_ext(n, 0.0);
for (const Load& ld : model_.loads()) {
f_ext[ld.dof] += ld.value;
}
for (const SpringSupport& sp : model_.springs()) {
f_ext[2 * sp.node] += sp.kappa * sp.settlement * sp.dir.x;
f_ext[2 * sp.node + 1] += sp.kappa * sp.settlement * sp.dir.y;
}
// ---- Precompute per-element geometry. ----
std::vector<double> Lv(ne), cv(ne), sv(ne), EAv(ne), epsv(ne);
std::vector<std::array<std::size_t, 4>> dofv(ne);
for (std::size_t e = 0; e < ne; ++e) {
const Element& el = elems[e];
Lv[e] = model_.element_length(e);
const Vec2 d = model_.element_direction(e);
cv[e] = d.x;
sv[e] = d.y;
EAv[e] = el.section.E * el.section.A;
epsv[e] = el.prestrain + el.alpha * el.dT;
dofv[e] = elem_dofs(el);
}
// Recover a member's total axial force (positive in tension) from a
// displacement field, using the ordinary elastic relation only.
auto recover_axial = [&](std::size_t e, const std::vector<double>& u) {
const double b[4] = {-cv[e], -sv[e], cv[e], sv[e]};
double delta = 0.0;
for (int i = 0; i < 4; ++i) {
delta += b[i] * u[dofv[e][i]];
}
return (EAv[e] / Lv[e]) * delta - EAv[e] * epsv[e];
};
// ---- Coupled active-set + initial-stress fixed-point iteration. ----
// We seek the state where the assumed member forces, the displacements they
// produce through the tangent stiffness, and the forces recovered from
// those displacements all coincide, with the cable/strut active set
// consistent with the recovered force signs.
std::vector<bool> active(ne, true); // start fully taut (stiffest state)
std::vector<double> N(ne, 0.0); // assumed total axial force (active)
std::vector<double> u(n, 0.0);
const int kMaxIter = 500;
for (int it = 0; it < kMaxIter; ++it) {
// Tangent = elastic(active) + springs + initial-stress(active).
DenseMatrix K = assemble_system(active);
for (std::size_t e = 0; e < ne; ++e) {
if (!active[e]) {
continue;
}
const double g[4] = {sv[e], -cv[e], -sv[e], cv[e]};
const double coef = N[e] / Lv[e];
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
K(dofv[e][i], dofv[e][j]) += coef * g[i] * g[j];
}
}
}
std::vector<double> F = prestrain_force(active);
for (std::size_t i = 0; i < n; ++i) {
F[i] += f_ext[i];
}
// Let a singular / non-positive-definite system propagate.
std::vector<double> u_new = solve_spd(K, F);
// Trial axial force every member would carry at this displacement.
std::vector<double> n_trial(ne, 0.0);
for (std::size_t e = 0; e < ne; ++e) {
n_trial[e] = recover_axial(e, u_new);
}
// Active-set update: a cable participates only in tension, a strut only
// in compression; a bar always participates.
std::vector<bool> new_active(ne, true);
for (std::size_t e = 0; e < ne; ++e) {
switch (elems[e].kind) {
case MemberKind::Bar:
new_active[e] = true;
break;
case MemberKind::Cable:
new_active[e] = (n_trial[e] > 0.0);
break;
case MemberKind::Strut:
new_active[e] = (n_trial[e] < 0.0);
break;
}
}
std::vector<double> n_new(ne, 0.0);
for (std::size_t e = 0; e < ne; ++e) {
if (new_active[e]) {
n_new[e] = n_trial[e];
}
}
const bool active_same = (new_active == active);
double dN = 0.0;
double scaleN = 0.0;
for (std::size_t e = 0; e < ne; ++e) {
dN = std::max(dN, std::abs(n_new[e] - N[e]));
scaleN = std::max(scaleN, std::abs(n_new[e]));
}
active = new_active;
N = n_new;
u = u_new;
if (active_same && dN <= 1e-10 * scaleN + 1e-9) {
break;
}
}
// ---- Assemble outputs. ----
SolveResult result;
result.displacements = u;
result.reactions.assign(n, 0.0);
for (const SpringSupport& 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;
}
result.axial_forces.assign(ne, 0.0);
result.utilization.assign(ne, 0.0);
result.active.assign(ne, true);
for (std::size_t e = 0; e < ne; ++e) {
result.active[e] = active[e];
if (active[e]) {
const double force = N[e];
result.axial_forces[e] = force;
result.utilization[e] = force / (kSigmaAllow * elems[e].section.A);
}
}
return result;
}
} // namespace truss2d
/opt/truss2d/src/solver.cpp
#include <array> #include <cmath>
#include <algorithm> #include <array> #include <cmath>
cmake -S . -B build -DCMAKE_BUILD_TYPE=Release >/tmp/cmake.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
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"
using namespace truss2d;
static int failures = 0;
static void check(bool ok, const char* msg, double a = 0, double b = 0) {
if (!ok) { printf("FAIL: %s (got %.8g, expect %.8g)\n", msg, a, b); ++failures; }
else { printf("ok : %s\n", msg); }
}
static bool near(double a, double b, double tol) { return std::abs(a - b) <= tol * (1 + std::abs(b)); }
// Residual of full equilibrium incl. geometric, springs, prestrain, loads.
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);
for (const auto& ld : m.loads()) resid[ld.dof] += ld.value;
for (std::size_t i = 0; i < n; ++i) resid[i] += r.reactions[i];
const auto& els = m.elements();
for (std::size_t e = 0; e < els.size(); ++e) {
if (!r.active[e]) continue;
Vec2 d = m.element_direction(e);
double c = d.x, s = d.y, L = m.element_length(e), N = r.axial_forces[e];
const auto& el = els[e];
// axial nodal forces: tension pulls ends toward each other
// force on n1 = +N*(c,s); on n2 = -N*(c,s)
resid[2*el.n1] += N*c; resid[2*el.n1+1] += N*s;
resid[2*el.n2] -= N*c; resid[2*el.n2+1] -= N*s;
// geometric transverse forces: (N/L) g g^T u, g={s,-c,-s,c}
double g[4] = {s, -c, -s, c};
std::size_t dof[4] = {2*el.n1, 2*el.n1+1, 2*el.n2, 2*el.n2+1};
double gu = 0; for (int i=0;i<4;i++) gu += g[i]*r.displacements[dof[i]];
for (int i=0;i<4;i++) resid[dof[i]] -= (N/L)*g[i]*gu;
}
double mx = 0; for (double v : resid) mx = std::max(mx, std::abs(v));
double scale = 0; for (const auto& ld : m.loads()) scale = std::max(scale, std::abs(ld.value));
for (double v : r.reactions) scale = std::max(scale, std::abs(v));
char buf[128]; snprintf(buf, sizeof buf, "equilibrium residual [%s]", tag);
check(mx <= 1e-6*(1+scale), buf, mx, 0);
}
int main() {
const double E = 2.0e11, A = 1.0e-3;
// ---- Test 1: single horizontal bar, axial load, soft spring at free node.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Bar);
m.add_spring(0,1,0,1e15); m.add_spring(0,0,1,1e15); m.add_spring(1,0,1,1e15);
m.add_load(2, 1e4); // node1 x
// node0 nearly fixed (stiff springs). bar EA/L = E*A/2 = 1e8.
// u1x = F/(k) approx F/(EA/L) = 1e4/1e8 = 1e-4 ; N = EA/L*u = 1e4 tension
auto r = StaticSolver(m).solve();
check(near(r.axial_forces[0], 1e4, 1e-3), "bar axial = load (tension)", r.axial_forces[0], 1e4);
check(near(r.displacements[2], 1e-4, 1e-3), "bar elongation", r.displacements[2], 1e-4);
check(r.active[0], "bar active");
check_equilibrium(m, r, "bar");
check(near(r.utilization[0], 1e4/(2.5e8*A), 1e-6), "utilization", r.utilization[0], 1e4/(2.5e8*A));
}
// ---- Test 2: prestrain sign. Bar manufactured too long (eps>0) -> compression.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Bar, 1e-3); // prestrain +1e-3
// both ends fully restrained by very stiff springs
m.add_spring(0,1,0,1e18); m.add_spring(0,0,1,1e18);
m.add_spring(1,1,0,1e18); m.add_spring(1,0,1,1e18);
auto r = StaticSolver(m).solve();
// fully restrained: N = -EA*eps = -2e11*1e-3*1e-3 = -2e5 (compression)
check(near(r.axial_forces[0], -E*A*1e-3, 2e-3), "prestrain too-long -> compression", r.axial_forces[0], -E*A*1e-3);
check_equilibrium(m, r, "prestrain");
}
// ---- Test 3: thermal heating -> compression (restrained).
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Bar, 0.0, 1.2e-5, 50.0);
m.add_spring(0,1,0,1e18); m.add_spring(0,0,1,1e18);
m.add_spring(1,1,0,1e18); m.add_spring(1,0,1,1e18);
auto r = StaticSolver(m).solve();
double expect = -E*A*(1.2e-5*50.0);
check(near(r.axial_forces[0], expect, 2e-3), "thermal heating -> compression", r.axial_forces[0], expect);
}
// ---- Test 4: cable goes slack under compression-inducing load.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Cable);
m.add_spring(0,1,0,1e15); m.add_spring(0,0,1,1e15); m.add_spring(1,0,1,1e15);
m.add_load(2, -1e4); // push node1 toward node0 -> would compress cable
auto r = StaticSolver(m).solve();
check(!r.active[0], "cable slack under compression");
check(r.axial_forces[0]==0.0, "slack cable zero force", r.axial_forces[0], 0);
check(r.utilization[0]==0.0, "slack cable zero util");
check_equilibrium(m, r, "cable-slack");
}
// ---- Test 5: cable taut under tension.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Cable);
m.add_spring(0,1,0,1e15); m.add_spring(0,0,1,1e15); m.add_spring(1,0,1,1e15);
m.add_load(2, 1e4);
auto r = StaticSolver(m).solve();
check(r.active[0], "cable taut under tension");
check(near(r.axial_forces[0], 1e4, 1e-3), "cable tension value", r.axial_forces[0], 1e4);
}
// ---- Test 6: strut separates under tension load.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Strut);
m.add_spring(0,1,0,1e15); m.add_spring(0,0,1,1e15); m.add_spring(1,0,1,1e15);
m.add_load(2, 1e4); // pull apart -> strut separates
auto r = StaticSolver(m).solve();
check(!r.active[0], "strut separates under tension");
check(r.axial_forces[0]==0.0, "separated strut zero force");
}
// ---- Test 7: settlement loads structure. Spring with settlement, restrained node.
{
Model m;
m.add_node(0,0);
// two orthogonal springs; one settles
m.add_spring(0, 1,0, 1e6, 0.01); // x-spring settlement 0.01 m, kappa 1e6
m.add_spring(0, 0,1, 1e6, 0.0);
// need an element + validate requires elements; add a tiny bar to node1 fully fixed
m.add_node(0,1);
m.add_element(0,1,Section{E,A},MemberKind::Bar);
m.add_spring(1,1,0,1e18); m.add_spring(1,0,1,1e18);
auto r = StaticSolver(m).solve();
// node0: x-spring wants node at 0.01. bar is vertical (no x-stiffness at node0 in x).
// Only x-spring acts in x at node0 -> node0 moves to settlement 0.01, reaction ~0.
check(near(r.displacements[0], 0.01, 1e-3), "settlement moves node", r.displacements[0], 0.01);
check_equilibrium(m, r, "settlement");
}
// ---- Test 8: geometric stiffness - taut cable resists transverse load.
// Pretensioned cable (prestrain negative -> tension), transverse point load.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
// cable too short -> tension. eps = -2e-3 -> N0 = +EA*2e-3 = 4e5 N
m.add_element(0,1,Section{E,A},MemberKind::Cable, -2e-3);
// pin both ends in x and y heavily, but allow node "mid"? Use 3 nodes.
// Simpler: anchor both ends, apply transverse load at... need interior node.
m.add_spring(0,1,0,1e18); m.add_spring(0,0,1,1e18);
m.add_spring(1,1,0,1e18); m.add_spring(1,0,1,1e18);
auto r = StaticSolver(m).solve();
check(r.axial_forces[0] > 0, "pretensioned cable tension", r.axial_forces[0], 0);
check(near(r.axial_forces[0], E*A*2e-3, 1e-2), "cable pretension value", r.axial_forces[0], E*A*2e-3);
}
// ---- Test 9: geometric effect on transverse stiffness with interior node.
// Two cable segments forming a taut string; transverse load at middle.
{
Model m;
m.add_node(0,0); m.add_node(1,0); m.add_node(2,0);
// pretension via thermal cooling on outer? Use prestrain to tension segments.
m.add_element(0,1,Section{E,A},MemberKind::Bar, -1e-3);
m.add_element(1,2,Section{E,A},MemberKind::Bar, -1e-3);
// anchor ends fully
m.add_spring(0,1,0,1e18); m.add_spring(0,0,1,1e18);
m.add_spring(2,1,0,1e18); m.add_spring(2,0,1,1e18);
// small spring at middle y to avoid singularity if no tension; but tension provides transverse stiffness
m.add_spring(1,0,1,1.0); // negligible
m.add_load(3, 1e3); // transverse (y) load at node1
auto r = StaticSolver(m).solve();
// Pretension T ~ EA*1e-3 = 2e5. Transverse stiffness of string ~ 2T/(L_half)...
// String: load P at center, two segments length 1. Transverse stiff = T*(1/L1 + 1/L2) = T*(1+1)=2T.
// disp = P/(2T) approx (geometric only). T approx 2e5 => disp ~ 1e3/(4e5)=2.5e-3
printf(" [string mid disp = %.6g, N0=%.6g]\n", r.displacements[3], r.axial_forces[0]);
check(r.displacements[3] > 0 && r.displacements[3] < 1e-1, "string transverse disp bounded", r.displacements[3], 0);
check_equilibrium(m, r, "string");
}
// ---- Test 10: skew roller (single inclined spring) finite compliance.
{
Model m;
m.add_node(0,0); m.add_node(2,0);
m.add_element(0,1,Section{E,A},MemberKind::Bar);
m.add_spring(0,1,0,1e18); m.add_spring(0,0,1,1e18);
double inv = 1.0/std::sqrt(2.0);
m.add_spring(1, inv, inv, 1e8); // 45-degree skew roller
m.add_load(2, 1e4); // x load at node1
auto r = StaticSolver(m).solve();
// reaction should be along (1,1)/sqrt2 only
double rx = r.reactions[2], ry = r.reactions[3];
// perpendicular component (-1,1)/sqrt2 should be ~0
double perp = (-rx + ry)*inv;
check(near(perp, 0.0, 1e-6)*(std::abs(rx)>1e-6||std::abs(ry)>1e-6) || std::abs(perp) < 1e-3*(std::abs(rx)+std::abs(ry)+1),
"skew roller reaction along dir only", perp, 0);
check_equilibrium(m, r, "skew");
}
printf("\n%s (%d failures)\n", failures==0?"ALL PASS":"SOME FAILED", failures);
return failures==0?0:1;
}
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 | head -20 && /tmp/verify
Exit 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 1: 1724 Aborted /tmp/verify [error] tool reported failure
/opt/truss2d/src/solver.cpp
std::vector<bool> active(ne, true); // start fully taut (stiffest state)
std::vector<double> N(ne, 0.0); // assumed total axial force (active)
std::vector<double> u(n, 0.0); std::vector<bool> active(ne, true); // start fully taut (stiffest state)
std::vector<double> u(n, 0.0);
// Seed the assumed axial force with the installed (prestress) force, i.e.
// the force each member carries at zero displacement, N0 = -E*A*eps. This
// gives a non-singular first tangent for genuinely pretensioned members
// whose only transverse stiffness comes from their own axial force.
std::vector<double> N(ne, 0.0);
for (std::size_t e = 0; e < ne; ++e) {
N[e] = -EAv[e] * epsv[e];
}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 | head && /tmp/verify
Exit 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 1: 1739 Aborted /tmp/verify [error] tool reported failure
cd /opt/truss2d && perl -0pi -e 's/(\{\s*\n\s*Model m;)/{ printf("--- entering a test ---\\n"); fflush(stdout);\n Model m;/g' verify.cpp && g++ -std=c++17 -Iinclude verify.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/verify 2>&1 | head && /tmp/verify 2>&1 | tail -8--- entering a test --- ok : prestrain too-long -> compression ok : equilibrium residual [prestrain] --- entering a test --- ok : thermal heating -> compression --- entering a test --- terminate called after throwing an instance of 'std::runtime_error' what(): solve_spd: matrix is singular or not positive-definite [stdout] --- entering a test --- ok : prestrain too-long -> compression ok : equilibrium residual [prestrain] --- entering a test --- ok : thermal heating -> compression --- entering a test --- terminate called after throwing an instance of 'std::runtime_error' what(): solve_spd: matrix is singular or not positive-definite
perl -0pi -e 's/(m\.add_load\(2, -1e4\); \/\/ push node1 toward node0 -> would compress cable)/m.add_spring(1,1,0,1e9); \/\/ keep node1 x supported when cable slack\n $1/; s/(m\.add_load\(2, 1e4\); \/\/ pull apart -> strut separates)/m.add_spring(1,1,0,1e9); \/\/ keep node1 x supported when strut separates\n $1/' verify.cpp && g++ -std=c++17 -Iinclude verify.cpp src/solver.cpp src/model.cpp src/dense_matrix.cpp -o /tmp/verify 2>&1 | head && /tmp/verify 2>&1 | grep -v "entering"
ok : bar axial = load (tension) ok : bar elongation ok : bar active ok : equilibrium residual [bar] ok : utilization ok : prestrain too-long -> compression ok : equilibrium residual [prestrain] ok : thermal heating -> compression ok : cable slack under compression ok : slack cable zero force ok : slack cable zero util ok : equilibrium residual [cable-slack] ok : cable taut under tension ok : cable tension value ok : strut separates under tension ok : separated strut zero force ok : settlement moves node ok : equilibrium residual [settlement] ok : pretensioned cable tension ok : cable pretension value [string mid disp = 0.00249999, N0=200000] ok : string transverse disp bounded ok : equilibrium residual [string] ok : skew roller reaction along dir only ok : equilibrium residual [skew] ALL PASS (0 failures) [stdout] ok : bar axial = load (tension) ok : bar elongation ok : bar active ok : equilibrium residual [bar] ok : utilization ok : prestrain too-long -> compression ok : equilibrium residual [prestrain] ok : thermal heating -> compression ok : cable slack under compression ok : slack cable zero force ok : slack cable zero util ok : equilibrium residual [cable-slack] ok : cable taut under tension ok : cable tension value ok : strut separates under tension ok : separated strut zero force ok : settlement moves node ok : equilibrium residual [settlement] ok : pretensioned cable tension ok : cable pretension value [string mid disp = 0.00249999, N0=200000] ok : string transverse disp bounded ok : equilibrium residual [string] ok : skew roller reaction along dir only ok : equilibrium residual [skew] ALL PASS (0 failures)
rm -f verify.cpp && cmake --build build --parallel >/tmp/b.log 2>&1 && echo BUILD_OK && cd build && ctest --output-on-failure 2>&1 | tail -5
BUILD_OK 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 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.qVuEPozZOp/truss2d/build_grade
== Building ==
[ 5%] Building CXX object CMakeFiles/truss2d.dir/src/dense_matrix.cpp.o
[ 10%] Building CXX object CMakeFiles/truss2d.dir/src/model.cpp.o
[ 15%] Building CXX object CMakeFiles/truss2d.dir/src/solver.cpp.o
[ 21%] Building CXX object CMakeFiles/truss2d.dir/src/io.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 tests/CMakeFiles/test_geometric.dir/test_geometric.cpp.o
[ 42%] Building CXX object CMakeFiles/truss2d_cli.dir/src/main.cpp.o
[ 47%] Building CXX object tests/CMakeFiles/test_unilateral.dir/test_unilateral.cpp.o
[ 52%] Building CXX object tests/CMakeFiles/test_soak.dir/test_soak.cpp.o
[ 57%] Building CXX object tests/CMakeFiles/test_degenerate.dir/test_degenerate.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_unilateral
[ 84%] Linking CXX executable test_soak
[ 84%] Built target test_unilateral
[ 89%] Linking CXX executable test_settlement
[ 89%] Built target test_soak
[ 89%] Built target test_settlement
[ 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.qVuEPozZOp/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_df713da845ac4223. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.
Trial trial_df713da845ac4223 · verifier authoritative; classifier explanatory.