tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it./opt/beamfd/src/solver.cpp
1 #include "beamfd/solver.hpp"
2
3 #include <cmath>
4 #include <cstddef>
5 #include <stdexcept>
6 #include <vector>
7
8 #include "beamfd/linalg.hpp"
9 #include "beamfd/types.hpp"
10
11 namespace beamfd {
12
13 // ============================================================================
14 // TODO(candidate): Implement the beam-bending finite-difference core.
15 //
16 // Two member functions below are stubs that currently return a zero deflection
17 // field and an empty/zero system, so every analysis is wrong and the grader
18 // fails. Replace the stub bodies of
19 //
20 // BeamSystem BeamSolver::assemble_system() const;
21 // BeamResult BeamSolver::solve() const;
22 //
23 // with correct implementations of the boundary-value problem specified in
24 // instruction.md. Do NOT change the public signatures declared in
25 // include/beamfd/solver.hpp, do NOT modify the recovery helpers below, and
26 // reuse the existing support layer (DenseMatrix, solve_general, and the Beam
27 // accessors EI_at / k_at / q_at / end_moment / applied_end_shear / left /
28 // right / dx / num_intervals / num_nodes / validate).
29 //
30 // The physics, the support and load semantics, the contract, and the I/O
31 // format are described in instruction.md. The required behaviour is enforced
32 // by a hidden grading suite (the shipped tests/ are only a smoke check); design
33 // a discretization that is at least second-order accurate and assemble the
34 // linear system A w = b for the nodal deflection, then solve it with
35 // solve_general. Call Beam::validate() at the start of solve() and let its
36 // exceptions (and any singular-system exception from solve_general) propagate.
37 // ============================================================================
38
39 BeamSystem BeamSolver::assemble_system() const {
40 // TODO(candidate): build and return the finite-difference system A w = b.
41 const std::size_t n = beam_.num_nodes();
42 BeamSystem sys;
43 sys.A = DenseMatrix(n, n); // all zeros -> singular / wrong
44 sys.b.assign(n, 0.0);
45 return sys;
46 }
47
48 BeamResult BeamSolver::solve() const {
49 // TODO(candidate): validate, assemble, solve, return the deflection field.
50 const std::size_t n = beam_.num_nodes();
51 BeamResult result;
52 result.deflection.assign(n, 0.0); // trivially zero -> wrong
53 return result;
54 }
55
56 // ----------------------------------------------------------------------------
57 // Recovery helpers (already implemented; do NOT modify). These differentiate a
58 // given deflection field so callers can recompute physical quantities (bending
59 // moment, shear) directly from a candidate result, honoring a variable EI(x).
60
61 namespace {
62
63 // Second derivative w''(x_i) by central difference (interior) / one-sided
64 // 2nd-order difference (ends).
65 double second_derivative(const std::vector<double>& w, std::size_t i, double h2) {
66 const std::size_t n = w.size();
67 if (i == 0) {
68 return (2.0 * w[0] - 5.0 * w[1] + 4.0 * w[2] - w[3]) / h2;
69 }
70 if (i == n - 1) {
71 return (2.0 * w[n - 1] - 5.0 * w[n - 2] + 4.0 * w[n - 3] - w[n - 4]) / h2;
72 }
73 return (w[i - 1] - 2.0 * w[i] + w[i + 1]) / h2;
74 }
75
76 } // namespace
77
78 std::vector<double> BeamSolver::bending_moment_field(
79 const std::vector<double>& w) const {
80 const std::size_t n = beam_.num_nodes();
81 if (w.size() != n) {
82 throw std::invalid_argument("bending_moment_field: deflection size mismatch");
83 }
84 const double h2 = beam_.dx() * beam_.dx();
85 std::vector<double> M(n, 0.0);
86 for (std::size_t i = 0; i < n; ++i) {
87 M[i] = beam_.EI_at(i) * second_derivative(w, i, h2);
88 }
89 return M;
90 }
91
92 std::vector<double> BeamSolver::shear_field(const std::vector<double>& w) const {
93 const std::size_t n = beam_.num_nodes();
94 if (w.size() != n) {
95 throw std::invalid_argument("shear_field: deflection size mismatch");
96 }
97 if (n < 5) {
98 throw std::invalid_argument("shear_field: need at least 5 nodes");
99 }
100 const double h = beam_.dx();
101 const double h2 = h * h;
102 std::vector<double> m(n, 0.0);
103 for (std::size_t j = 0; j < n; ++j) {
104 m[j] = beam_.EI_at(j) * second_derivative(w, j, h2);
105 }
106 std::vector<double> V(n, 0.0);
107 for (std::size_t i = 0; i < n; ++i) {
108 if (i == 0) {
109 V[i] = (-3.0 * m[0] + 4.0 * m[1] - m[2]) / (2.0 * h);
110 } else if (i == n - 1) {
111 V[i] = (3.0 * m[n - 1] - 4.0 * m[n - 2] + m[n - 3]) / (2.0 * h);
112 } else {
113 V[i] = (m[i + 1] - m[i - 1]) / (2.0 * h);
114 }
115 }
116 return V;
117 }
118
119 } // namespace beamfd
120
/opt/beamfd/include/beamfd/solver.hpp
1 #ifndef BEAMFD_SOLVER_HPP
2 #define BEAMFD_SOLVER_HPP
3
4 #include <cstddef>
5 #include <vector>
6
7 #include "beamfd/beam.hpp"
8 #include "beamfd/linalg.hpp"
9
10 namespace beamfd {
11
12 /// The assembled finite-difference linear system A w = b for a beam.
13 /// `A` has size num_nodes x num_nodes and `b` has length num_nodes; the
14 /// unknown w is the nodal transverse deflection field. Exposed so tests can
15 /// check the discrete equilibrium residual directly.
16 struct BeamSystem {
17 DenseMatrix A;
18 std::vector<double> b;
19 };
20
21 /// Result of a static beam-bending analysis.
22 struct BeamResult {
23 /// Nodal transverse deflection w_i [m], length == beam.num_nodes(),
24 /// ordered from x = 0 (i = 0) to x = L (i = num_intervals).
25 std::vector<double> deflection;
26 };
27
28 /// Static bending solver for an Euler-Bernoulli beam with (possibly) variable
29 /// flexural rigidity and an optional elastic foundation. The continuum
30 /// boundary-value problem and the support/load semantics are specified in
31 /// instruction.md; choosing and assembling a suitable finite-difference
32 /// discretization of it, and solving the resulting linear system, is the work
33 /// of this class.
34 class BeamSolver {
35 public:
36 explicit BeamSolver(const Beam& beam) : beam_(beam) {}
37
38 /// Run the full analysis. Calls Beam::validate() first and propagates any
39 /// exception it throws. Throws std::runtime_error if the assembled system
40 /// is singular.
41 BeamResult solve() const;
42
43 /// Assemble the finite-difference system A w = b. Exposed for testing and
44 /// reuse (the discrete equilibrium-residual invariant checks A w - b ~ 0 at
45 /// the interior nodes).
46 BeamSystem assemble_system() const;
47
48 // ---- Recovery helpers (fully implemented; operate on a deflection field).
49 // These let the caller recompute physical quantities directly from a
50 // candidate deflection vector, independent of how it was produced.
51
52 /// Bending moment M_i = EI(x_i) * w''(x_i) [N*m] via a central second
53 /// difference at interior nodes and a one-sided second difference at the
54 /// ends. `w` must have length num_nodes(). Throws std::invalid_argument
55 /// otherwise.
56 std::vector<double> bending_moment_field(const std::vector<double>& w) const;
57
58 /// Shear force V_i = (EI w'')'(x_i) [N] via finite differences of the
59 /// nodal bending moment. `w` must have length num_nodes(). Throws
60 /// std::invalid_argument otherwise.
61 std::vector<double> shear_field(const std::vector<double>& w) const;
62
63 private:
64 const Beam& beam_;
65 };
66
67 } // namespace beamfd
68
69 #endif // BEAMFD_SOLVER_HPP
70
/opt/beamfd/include/beamfd/beam.hpp
1 #ifndef BEAMFD_BEAM_HPP
2 #define BEAMFD_BEAM_HPP
3
4 #include <cstddef>
5 #include <utility>
6 #include <vector>
7
8 #include "beamfd/types.hpp"
9
10 namespace beamfd {
11
12 /// A 1D Euler-Bernoulli beam discretized on a uniform grid, with a possibly
13 /// non-uniform flexural rigidity EI(x), an optional Winkler elastic foundation
14 /// k(x), a (possibly spatially varying) transverse load q(x), and optional
15 /// applied force/moment at free ends.
16 ///
17 /// This is a plain data container plus light validation. The numerical core
18 /// (assembling and solving the finite-difference system for the deflection
19 /// field) lives in BeamSolver (see solver.hpp).
20 ///
21 /// Geometry / grid:
22 /// - The beam occupies x in [0, L], divided into `num_intervals` equal cells,
23 /// giving num_nodes() = num_intervals + 1 grid points at x_i = i * dx,
24 /// dx = L / num_intervals, for i = 0 .. num_intervals.
25 ///
26 /// Fields are stored per node (length num_nodes()):
27 /// - EI_at(i) flexural rigidity at node i [N*m^2] (> 0)
28 /// - k_at(i) Winkler foundation modulus at node i [N/m^2] (>= 0; 0 = none)
29 /// - q_at(i) distributed transverse load at node i [N/m]
30 /// plus optional applied actions at free ends (force [N] and moment [N*m]).
31 class Beam {
32 public:
33 /// Construct a beam of length `length` [m] with a uniform flexural rigidity
34 /// `EI` [N*m^2], discretized into `num_intervals` equal cells, with the
35 /// given end supports. EI(x) is initialised constant, k(x) = 0, q(x) = 0.
36 /// Throws std::invalid_argument if length or EI is non-positive or
37 /// num_intervals < 2.
38 Beam(double length, double EI, std::size_t num_intervals, Support left,
39 Support right);
40
41 // ---- Field setters -------------------------------------------------------
42
43 /// Set the nodal flexural-rigidity field EI(x_i). Size must equal
44 /// num_nodes(); every value must be > 0. Throws std::invalid_argument.
45 void set_ei_nodal(const std::vector<double>& ei);
46
47 /// Set EI(x) from piecewise-linear control points (x, value), sampled at
48 /// each node. Points are taken in the given order; x outside the range is
49 /// clamped to the nearest endpoint value. Every sampled value must be > 0.
50 void set_ei_profile(const std::vector<std::pair<double, double>>& points);
51
52 /// Set the nodal Winkler foundation field k(x_i) >= 0. Size == num_nodes().
53 void set_foundation_nodal(const std::vector<double>& k);
54
55 /// Set k(x) from piecewise-linear control points (x, value).
56 void set_foundation_profile(
57 const std::vector<std::pair<double, double>>& points);
58
59 /// Set the nodal distributed-load field q(x_i). Size == num_nodes().
60 void set_q_nodal(const std::vector<double>& q);
61
62 /// Set a uniform distributed load q [N/m] over the whole span (overwrites
63 /// the load field).
64 void set_distributed_load(double q);
65
66 /// Add a piecewise-linear distributed-load segment ramping from q0 at x0 to
67 /// q1 at x1 [N/m] to the existing load field. Segments are additive.
68 void add_load_segment(double x0, double x1, double q0, double q1);
69
70 /// Apply a transverse force P [N] at a free end (`at_left_end` -> x = 0,
71 /// else x = L). Throws std::runtime_error if that end is not Free.
72 void set_end_load(double P, bool at_left_end);
73
74 /// Apply a concentrated moment M [N*m] at a free end. Throws
75 /// std::runtime_error if that end is not Free.
76 void set_end_moment(double M, bool at_left_end);
77
78 // ---- Accessors -----------------------------------------------------------
79
80 double length() const { return length_; }
81 std::size_t num_intervals() const { return num_intervals_; }
82 std::size_t num_nodes() const { return num_intervals_ + 1; }
83 double dx() const { return length_ / static_cast<double>(num_intervals_); }
84 double node_x(std::size_t i) const;
85
86 Support left() const { return left_; }
87 Support right() const { return right_; }
88
89 double EI_at(std::size_t i) const; ///< nodal flexural rigidity [N*m^2]
90 double k_at(std::size_t i) const; ///< nodal foundation modulus [N/m^2]
91 double q_at(std::size_t i) const; ///< nodal distributed load [N/m]
92
93 /// A representative (maximum nodal) flexural rigidity [N*m^2], used as a
94 /// scale for residual normalisation. Equals the constant EI for a uniform
95 /// beam.
96 double EI() const;
97
98 /// True if any nodal foundation modulus is strictly positive.
99 bool has_foundation() const;
100
101 /// Applied end shear V at a free end (`left_end` -> x = 0). A transverse
102 /// force P at a free end contributes V = -P; 0 if no force is applied.
103 double applied_end_shear(bool left_end) const;
104
105 /// Applied end moment M [N*m] at a free end (0 if none).
106 double end_moment(bool left_end) const;
107
108 /// True if any end force has been applied.
109 bool has_end_load() const;
110
111 /// Throws std::runtime_error if the support / foundation combination cannot
112 /// suppress rigid-body motion (a free end opposite a non-clamped end, or
113 /// two free ends, is a mechanism UNLESS an elastic foundation is present).
114 void validate() const;
115
116 private:
117 static std::size_t end_index(bool left_end) { return left_end ? 0u : 1u; }
118
119 double length_{0.0};
120 std::size_t num_intervals_{0};
121 Support left_{Support::Clamped};
122 Support right_{Support::Free};
123 std::vector<double> ei_; // nodal EI, length num_nodes()
124 std::vector<double> k_; // nodal foundation, length num_nodes()
125 std::vector<double> q_; // nodal load, length num_nodes()
126 double force_[2]{0.0, 0.0}; // applied transverse force [left, right]
127 double moment_[2]{0.0, 0.0}; // applied moment [left, right]
128 };
129
130 } // namespace beamfd
131
132 #endif // BEAMFD_BEAM_HPP
133
/opt/beamfd/include/beamfd/linalg.hpp
1 #ifndef BEAMFD_LINALG_HPP
2 #define BEAMFD_LINALG_HPP
3
4 #include <cstddef>
5 #include <stdexcept>
6 #include <vector>
7
8 namespace beamfd {
9
10 /// A small, row-major dense matrix of doubles.
11 ///
12 /// Part of the engine's linear-algebra support layer; fully implemented. The
13 /// beam solver uses it to hold the finite-difference system matrix A in
14 /// A w = b. Unlike a structural stiffness matrix, A here is generally NON
15 /// symmetric (boundary-condition rows are one-sided difference stencils), so
16 /// the solve uses a general LU factorization rather than a Cholesky/LDL^T.
17 class DenseMatrix {
18 public:
19 DenseMatrix() = default;
20
21 DenseMatrix(std::size_t rows, std::size_t cols)
22 : rows_(rows), cols_(cols), data_(rows * cols, 0.0) {}
23
24 std::size_t rows() const { return rows_; }
25 std::size_t cols() const { return cols_; }
26
27 double& operator()(std::size_t r, std::size_t c) {
28 return data_[r * cols_ + c];
29 }
30 double operator()(std::size_t r, std::size_t c) const {
31 return data_[r * cols_ + c];
32 }
33
34 void fill(double v) {
35 for (auto& x : data_) x = v;
36 }
37
38 private:
39 std::size_t rows_{0};
40 std::size_t cols_{0};
41 std::vector<double> data_;
42 };
43
44 /// Solve the general (possibly non-symmetric) linear system A x = b by LU
45 /// factorization with partial (row) pivoting.
46 ///
47 /// `A` is the n-by-n system matrix and `b` is the right-hand side of length n.
48 /// Returns the solution vector x of length n.
49 ///
50 /// Throws std::runtime_error if A is not square, if the dimensions are
51 /// inconsistent, or if A is detected to be singular (a pivot column is
52 /// numerically zero), which is how an under-/over-determined boundary-value
53 /// problem surfaces.
54 std::vector<double> solve_general(const DenseMatrix& A,
55 const std::vector<double>& b);
56
57 } // namespace beamfd
58
59 #endif // BEAMFD_LINALG_HPP
60
/opt/beamfd/include/beamfd/types.hpp
1 #ifndef BEAMFD_TYPES_HPP
2 #define BEAMFD_TYPES_HPP
3
4 #include <cstddef>
5
6 namespace beamfd {
7
8 /// Type of support condition applied at one end of the beam.
9 ///
10 /// - Clamped (built-in / fixed): deflection and slope are both zero
11 /// (w = 0, w' = 0).
12 /// - Pinned (simple support): deflection is zero and the bending moment
13 /// is zero (w = 0, M = 0).
14 /// - Free: the bending moment and shear take their
15 /// applied values (M = M_applied, V = V_applied), both zero when no end
16 /// action is applied.
17 ///
18 /// See instruction.md for the continuum boundary-value problem these encode.
19 enum class Support {
20 Clamped,
21 Pinned,
22 Free,
23 };
24
25 } // namespace beamfd
26
27 #endif // BEAMFD_TYPES_HPP
28
/opt/beamfd/src/beam.cpp
1 #include "beamfd/beam.hpp"
2
3 #include <algorithm>
4 #include <stdexcept>
5
6 namespace beamfd {
7
8 namespace {
9
10 // Piecewise-linear interpolation of control points (x, value) at coordinate x.
11 // Points are used in the given order (assumed nondecreasing in x); x outside
12 // the range is clamped to the nearest endpoint.
13 double interp(const std::vector<std::pair<double, double>>& pts, double x) {
14 if (pts.empty()) {
15 throw std::invalid_argument("Beam: empty profile control points");
16 }
17 if (x <= pts.front().first) return pts.front().second;
18 if (x >= pts.back().first) return pts.back().second;
19 for (std::size_t s = 1; s < pts.size(); ++s) {
20 const double x0 = pts[s - 1].first, x1 = pts[s].first;
21 if (x <= x1) {
22 const double t = (x1 > x0) ? (x - x0) / (x1 - x0) : 0.0;
23 return pts[s - 1].second + t * (pts[s].second - pts[s - 1].second);
24 }
25 }
26 return pts.back().second;
27 }
28
29 } // namespace
30
31 Beam::Beam(double length, double EI, std::size_t num_intervals, Support left,
32 Support right)
33 : length_(length),
34 num_intervals_(num_intervals),
35 left_(left),
36 right_(right) {
37 if (length_ <= 0.0) {
38 throw std::invalid_argument("Beam: length must be positive");
39 }
40 if (EI <= 0.0) {
41 throw std::invalid_argument("Beam: EI must be positive");
42 }
43 if (num_intervals_ < 2) {
44 throw std::invalid_argument("Beam: need at least 2 intervals");
45 }
46 const std::size_t n = num_nodes();
47 ei_.assign(n, EI);
48 k_.assign(n, 0.0);
49 q_.assign(n, 0.0);
50 }
51
52 void Beam::set_ei_nodal(const std::vector<double>& ei) {
53 if (ei.size() != num_nodes()) {
54 throw std::invalid_argument("Beam::set_ei_nodal: size mismatch");
55 }
56 for (double v : ei) {
57 if (v <= 0.0) {
58 throw std::invalid_argument("Beam::set_ei_nodal: EI must be positive");
59 }
60 }
61 ei_ = ei;
62 }
63
64 void Beam::set_ei_profile(const std::vector<std::pair<double, double>>& points) {
65 std::vector<double> ei(num_nodes());
66 for (std::size_t i = 0; i < num_nodes(); ++i) ei[i] = interp(points, node_x(i));
67 set_ei_nodal(ei);
68 }
69
70 void Beam::set_foundation_nodal(const std::vector<double>& k) {
71 if (k.size() != num_nodes()) {
72 throw std::invalid_argument("Beam::set_foundation_nodal: size mismatch");
73 }
74 for (double v : k) {
75 if (v < 0.0) {
76 throw std::invalid_argument(
77 "Beam::set_foundation_nodal: k must be non-negative");
78 }
79 }
80 k_ = k;
81 }
82
83 void Beam::set_foundation_profile(
84 const std::vector<std::pair<double, double>>& points) {
85 std::vector<double> k(num_nodes());
86 for (std::size_t i = 0; i < num_nodes(); ++i) k[i] = interp(points, node_x(i));
87 set_foundation_nodal(k);
88 }
89
90 void Beam::set_q_nodal(const std::vector<double>& q) {
91 if (q.size() != num_nodes()) {
92 throw std::invalid_argument("Beam::set_q_nodal: size mismatch");
93 }
94 q_ = q;
95 }
96
97 void Beam::set_distributed_load(double q) { q_.assign(num_nodes(), q); }
98
99 void Beam::add_load_segment(double x0, double x1, double q0, double q1) {
100 if (x1 < x0) {
101 std::swap(x0, x1);
102 std::swap(q0, q1);
103 }
104 for (std::size_t i = 0; i < num_nodes(); ++i) {
105 const double x = node_x(i);
106 if (x < x0 || x > x1) continue;
107 const double t = (x1 > x0) ? (x - x0) / (x1 - x0) : 0.0;
108 q_[i] += q0 + t * (q1 - q0);
109 }
110 }
111
112 void Beam::set_end_load(double P, bool at_left_end) {
113 const Support s = at_left_end ? left_ : right_;
114 if (s != Support::Free) {
115 throw std::runtime_error(
116 "Beam::set_end_load: end load may only be applied at a free end");
117 }
118 force_[end_index(at_left_end)] = P;
119 }
120
121 void Beam::set_end_moment(double M, bool at_left_end) {
122 const Support s = at_left_end ? left_ : right_;
123 if (s != Support::Free) {
124 throw std::runtime_error(
125 "Beam::set_end_moment: end moment may only be applied at a free end");
126 }
127 moment_[end_index(at_left_end)] = M;
128 }
129
130 double Beam::node_x(std::size_t i) const {
131 if (i > num_intervals_) {
132 throw std::out_of_range("Beam::node_x: node index out of range");
133 }
134 return static_cast<double>(i) * dx();
135 }
136
137 double Beam::EI_at(std::size_t i) const {
138 if (i >= ei_.size()) throw std::out_of_range("Beam::EI_at: index out of range");
139 return ei_[i];
140 }
141
142 double Beam::k_at(std::size_t i) const {
143 if (i >= k_.size()) throw std::out_of_range("Beam::k_at: index out of range");
144 return k_[i];
145 }
146
147 double Beam::q_at(std::size_t i) const {
148 if (i >= q_.size()) throw std::out_of_range("Beam::q_at: index out of range");
149 return q_[i];
150 }
151
152 double Beam::EI() const {
153 double m = 0.0;
154 for (double v : ei_) m = std::max(m, v);
155 return m;
156 }
157
158 bool Beam::has_foundation() const {
159 for (double v : k_) {
160 if (v > 0.0) return true;
161 }
162 return false;
163 }
164
165 double Beam::applied_end_shear(bool left_end) const {
166 return -force_[end_index(left_end)];
167 }
168
169 double Beam::end_moment(bool left_end) const { return moment_[end_index(left_end)]; }
170
171 bool Beam::has_end_load() const { return force_[0] != 0.0 || force_[1] != 0.0; }
172
173 void Beam::validate() const {
174 const bool left_free = (left_ == Support::Free);
175 const bool right_free = (right_ == Support::Free);
176
177 // An elastic foundation supplies distributed restraint that removes the
178 // rigid-body modes, so any support combination is well posed when present.
179 if (has_foundation()) return;
180
181 if (left_free && right_free) {
182 throw std::runtime_error("Beam::validate: free-free beam is a mechanism");
183 }
184 if (left_free && right_ != Support::Clamped) {
185 throw std::runtime_error(
186 "Beam::validate: a free end requires a clamped opposite end");
187 }
188 if (right_free && left_ != Support::Clamped) {
189 throw std::runtime_error(
190 "Beam::validate: a free end requires a clamped opposite end");
191 }
192 }
193
194 } // namespace beamfd
195
List tests and project root
ls -R /opt/beamfd/tests 2>/dev/null; echo "---"; ls /opt/beamfd
/opt/beamfd/tests: CMakeLists.txt test_smoke.cpp test_util.hpp --- CMakeLists.txt examples include src tests [stdout] /opt/beamfd/tests: CMakeLists.txt test_smoke.cpp test_util.hpp --- CMakeLists.txt examples include src tests
/opt/beamfd/tests/test_smoke.cpp
1 // Smoke test for the beamfd project: a minimal, non-leaky sanity check so the
2 // project compiles and a solver gets quick feedback. It asserts only generic
3 // properties (finite field, pinned ends fixed, a non-trivial deflection, and a
4 // small interior discrete-equilibrium residual) and contains NO closed-form
5 // answer. The authoritative grading is performed by a separate hidden suite.
6
7 #include <algorithm>
8 #include <cmath>
9
10 #include "beamfd/beam.hpp"
11 #include "beamfd/solver.hpp"
12 #include "test_util.hpp"
13
14 using namespace beamfd;
15
16 BEAMFD_TEST("smoke_pinned_udl_sane") {
17 Beam beam(2.0, 1000.0, 20, Support::Pinned, Support::Pinned);
18 beam.set_distributed_load(5.0);
19 BeamSolver solver(beam);
20 BeamResult r = solver.solve();
21 const std::size_t n = beam.num_nodes();
22
23 beamfd_test::expect(r.deflection.size() == n, "deflection has num_nodes entries");
24 for (double w : r.deflection) {
25 beamfd_test::expect(std::isfinite(w), "deflection is finite");
26 }
27 beamfd_test::expect_near(r.deflection[0], 0.0, 1e-9, "left pin fixed");
28 beamfd_test::expect_near(r.deflection[n - 1], 0.0, 1e-9, "right pin fixed");
29 beamfd_test::expect(r.deflection[n / 2] > 0.0, "mid-span deflects under load");
30
31 // Interior discrete-equilibrium residual A w - b ~ 0 (relative to scale).
32 BeamSystem sys = solver.assemble_system();
33 double scale = 0.0;
34 for (double w : r.deflection) scale = std::max(scale, std::fabs(w));
35 const double c4 = beam.EI() / std::pow(beam.dx(), 4);
36 for (std::size_t i = 2; i + 2 < n; ++i) {
37 double res = -sys.b[i];
38 for (std::size_t j = 0; j < n; ++j) res += sys.A(i, j) * r.deflection[j];
39 beamfd_test::expect(std::fabs(res) <= 1e-6 * (c4 * scale) + 1e-9,
40 "interior equilibrium residual is small");
41 }
42 }
43
44 BEAMFD_TEST_MAIN()
45
/opt/beamfd/tests/test_util.hpp
1 #ifndef BEAMFD_TEST_UTIL_HPP
2 #define BEAMFD_TEST_UTIL_HPP
3
4 // Minimal dependency-free test harness for the beamfd suite.
5 //
6 // Each test executable defines test functions and registers them with
7 // BEAMFD_TEST(name) { ... }. main() (provided by BEAMFD_TEST_MAIN) runs every
8 // registered test and returns non-zero if any assertion fails, which CTest
9 // interprets as a failure.
10
11 #include <cmath>
12 #include <cstddef>
13 #include <functional>
14 #include <iostream>
15 #include <string>
16 #include <vector>
17
18 namespace beamfd_test {
19
20 struct Case {
21 std::string name;
22 std::function<void()> fn;
23 };
24
25 inline std::vector<Case>& registry() {
26 static std::vector<Case> cases;
27 return cases;
28 }
29
30 struct Registrar {
31 Registrar(const std::string& name, std::function<void()> fn) {
32 registry().push_back(Case{name, std::move(fn)});
33 }
34 };
35
36 // Thrown by an assertion failure to abort the current test case.
37 struct AssertionError {
38 std::string message;
39 };
40
41 inline void expect(bool cond, const std::string& what) {
42 if (!cond) {
43 throw AssertionError{what};
44 }
45 }
46
47 inline void expect_near(double got, double want, double tol, const std::string& what) {
48 if (std::fabs(got - want) > tol) {
49 throw AssertionError{what + " (got " + std::to_string(got) +
50 ", want " + std::to_string(want) +
51 ", tol " + std::to_string(tol) + ")"};
52 }
53 }
54
55 // Relative-error check (with an absolute floor) for quantities whose scale
56 // varies widely across cases.
57 inline void expect_rel(double got, double want, double rel_tol,
58 const std::string& what) {
59 const double denom = std::fabs(want) > 1e-300 ? std::fabs(want) : 1.0;
60 if (std::fabs(got - want) / denom > rel_tol) {
61 throw AssertionError{what + " (got " + std::to_string(got) +
62 ", want " + std::to_string(want) +
63 ", rel_tol " + std::to_string(rel_tol) + ")"};
64 }
65 }
66
67 inline int run_all() {
68 int failures = 0;
69 for (const auto& c : registry()) {
70 try {
71 c.fn();
72 std::cout << "[ PASS ] " << c.name << "\n";
73 } catch (const AssertionError& e) {
74 std::cout << "[ FAIL ] " << c.name << ": " << e.message << "\n";
75 ++failures;
76 } catch (const std::exception& e) {
77 std::cout << "[ FAIL ] " << c.name
78 << ": unexpected exception: " << e.what() << "\n";
79 ++failures;
80 } catch (...) {
81 std::cout << "[ FAIL ] " << c.name << ": unknown exception\n";
82 ++failures;
83 }
84 }
85 std::cout << "----\n"
86 << (registry().size() - failures) << "/" << registry().size()
87 << " tests passed\n";
88 return failures == 0 ? 0 : 1;
89 }
90
91 } // namespace beamfd_test
92
93 #define BEAMFD_CONCAT_INNER(a, b) a##b
94 #define BEAMFD_CONCAT(a, b) BEAMFD_CONCAT_INNER(a, b)
95
96 #define BEAMFD_TEST(NAME) \
97 static void BEAMFD_CONCAT(beamfd_test_fn_, __LINE__)(); \
98 static ::beamfd_test::Registrar BEAMFD_CONCAT(beamfd_test_reg_, \
99 __LINE__){ \
100 NAME, &BEAMFD_CONCAT(beamfd_test_fn_, __LINE__)}; \
101 static void BEAMFD_CONCAT(beamfd_test_fn_, __LINE__)()
102
103 #define BEAMFD_TEST_MAIN() \
104 int main() { return ::beamfd_test::run_all(); }
105
106 #endif // BEAMFD_TEST_UTIL_HPP
107
Inspect build config and examples
cat /opt/beamfd/CMakeLists.txt; echo "===EXAMPLES==="; ls /opt/beamfd/examples; echo "==="; head -40 /opt/beamfd/examples/* 2>/dev/null | head -80
cmake_minimum_required(VERSION 3.16)
project(beamfd LANGUAGES CXX)
set(CMAKE_CXX_STANDARD 17)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
set(CMAKE_CXX_EXTENSIONS OFF)
if(NOT CMAKE_BUILD_TYPE)
set(CMAKE_BUILD_TYPE Release)
endif()
add_compile_options(-Wall -Wextra)
# --- Core library -----------------------------------------------------------
add_library(beamfd
src/linalg.cpp
src/beam.cpp
src/solver.cpp
src/io.cpp
)
target_include_directories(beamfd PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/include)
# --- Demo CLI ---------------------------------------------------------------
add_executable(beamfd_cli src/main.cpp)
target_link_libraries(beamfd_cli PRIVATE beamfd)
# --- Tests ------------------------------------------------------------------
enable_testing()
add_subdirectory(tests)
===EXAMPLES===
cantilever_tip.beam
===
# Cantilever beam with a downward point load at the free tip.
# Clamped (built-in) at x = 0, free at x = L.
length 3.0 # span [m]
ei 2.0e6 # flexural rigidity EI [N*m^2]
cells 200 # number of equal finite-difference intervals
# Left end clamped, right end free.
support clamped free
# Downward point load of 1 kN at the free right tip.
endload right 1000.0
[stdout]
cmake_minimum_required(VERSION 3.16)
project(beamfd LANGUAGES CXX)
set(CMAKE_CXX_STANDARD 17)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
set(CMAKE_CXX_EXTENSIONS OFF)
if(NOT CMAKE_BUILD_TYPE)
set(CMAKE_BUILD_TYPE Release)
endif()
add_compile_options(-Wall -Wextra)
# --- Core library -----------------------------------------------------------
add_library(beamfd
src/linalg.cpp
src/beam.cpp
src/solver.cpp
src/io.cpp
)
target_include_directories(beamfd PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/include)
# --- Demo CLI ---------------------------------------------------------------
add_executable(beamfd_cli src/main.cpp)
target_link_libraries(beamfd_cli PRIVATE beamfd)
# --- Tests ------------------------------------------------------------------
enable_testing()
add_subdirectory(tests)
===EXAMPLES===
cantilever_tip.beam
===
# Cantilever beam with a downward point load at the free tip.
# Clamped (built-in) at x = 0, free at x = L.
length 3.0 # span [m]
ei 2.0e6 # flexural rigidity EI [N*m^2]
cells 200 # number of equal finite-difference intervals
# Left end clamped, right end free.
support clamped free
# Downward point load of 1 kN at the free right tip.
endload right 1000.0/opt/beamfd/src/solver.cpp
BeamSystem BeamSolver::assemble_system() const {
// TODO(candidate): build and return the finite-difference system A w = b.
const std::size_t n = beam_.num_nodes();
BeamSystem sys;
sys.A = DenseMatrix(n, n); // all zeros -> singular / wrong
sys.b.assign(n, 0.0);
return sys;
}
BeamResult BeamSolver::solve() const {
// TODO(candidate): validate, assemble, solve, return the deflection field.
const std::size_t n = beam_.num_nodes();
BeamResult result;
result.deflection.assign(n, 0.0); // trivially zero -> wrong
return result;
}BeamSystem BeamSolver::assemble_system() const {
// Second-order finite-difference discretization of the conservative
// Euler-Bernoulli equation
//
// d^2/dx^2 ( EI(x) w''(x) ) + k(x) w(x) = q(x)
//
// on the uniform grid x_i = i*dx, i = 0..N (n = N+1 nodes). We work with the
// discrete nodal bending moment
//
// m_j = EI_j * (w_{j-1} - 2 w_j + w_{j+1}) / dx^2 (= EI_j w''_j),
//
// so the operator becomes the nested second difference
//
// (m_{i-1} - 2 m_i + m_{i+1}) / dx^2 + k_i w_i = q_i,
//
// which is a 5-point stencil in w with spatially varying EI. This PDE row is
// enforced at the interior nodes i = 1..N-1. The two boundary rows (0 and N)
// and the ghost nodes w_{-1}, w_{N+1} appearing in the PDE rows nearest each
// end are fixed by that end's two support conditions: one condition supplies
// the boundary row, the other eliminates the ghost (folded into m_0 / m_N).
const std::size_t n = beam_.num_nodes();
const std::size_t N = beam_.num_intervals(); // last node index, n == N+1
const double h = beam_.dx();
const double h2 = h * h;
BeamSystem sys;
sys.A = DenseMatrix(n, n);
sys.b.assign(n, 0.0);
DenseMatrix& A = sys.A;
std::vector<double>& b = sys.b;
const Support Lsup = beam_.left();
const Support Rsup = beam_.right();
const double M_L = beam_.end_moment(true); // applied moment, left
const double M_R = beam_.end_moment(false); // applied moment, right
const double V_L = beam_.applied_end_shear(true); // applied shear, left
const double V_R = beam_.applied_end_shear(false); // applied shear, right
// Add the interior discrete moment m_j to row i, scaled by f.
// m_j = EI_j/h^2 (w_{j-1} - 2 w_j + w_{j+1}); valid for 1 <= j <= N-1.
auto add_interior_moment = [&](std::size_t i, std::size_t j, double f) {
const double c = f * beam_.EI_at(j) / h2;
A(i, j - 1) += c;
A(i, j) += -2.0 * c;
A(i, j + 1) += c;
};
// Add the left boundary moment m_0 to row i (scaled by f), applying the
// ghost (w_{-1}) elimination implied by the left support.
auto add_left_moment = [&](std::size_t i, double f) {
const double c = f * beam_.EI_at(0) / h2;
switch (Lsup) {
case Support::Clamped: // w' = 0 -> w_{-1} = w_1 -> m_0 = EI_0/h^2 (2w_1 - 2w_0)
A(i, 0) += -2.0 * c;
A(i, 1) += 2.0 * c;
break;
case Support::Pinned: // M = 0 -> m_0 = 0
break;
case Support::Free: // M = M_L (known) -> m_0 = M_L, move to RHS
b[i] -= f * M_L;
break;
}
};
// Add the right boundary moment m_N to row i (scaled by f), applying the
// ghost (w_{N+1}) elimination implied by the right support.
auto add_right_moment = [&](std::size_t i, double f) {
const double c = f * beam_.EI_at(N) / h2;
switch (Rsup) {
case Support::Clamped: // w_{N+1} = w_{N-1} -> m_N = EI_N/h^2 (2w_{N-1} - 2w_N)
A(i, N) += -2.0 * c;
A(i, N - 1) += 2.0 * c;
break;
case Support::Pinned:
break;
case Support::Free:
b[i] -= f * M_R;
break;
}
};
// Dispatch a moment node j (possibly a boundary node) into row i, scale f.
auto add_moment = [&](std::size_t i, std::size_t j, double f) {
if (j == 0) {
add_left_moment(i, f);
} else if (j == N) {
add_right_moment(i, f);
} else {
add_interior_moment(i, j, f);
}
};
// --- Interior PDE rows: govern nodes i = 1..N-1.
const double inv_h2 = 1.0 / h2;
for (std::size_t i = 1; i <= N - 1; ++i) {
add_moment(i, i - 1, inv_h2);
add_moment(i, i, -2.0 * inv_h2);
add_moment(i, i + 1, inv_h2);
A(i, i) += beam_.k_at(i);
b[i] += beam_.q_at(i);
}
// --- Left boundary row (row 0).
switch (Lsup) {
case Support::Clamped:
case Support::Pinned:
A(0, 0) = 1.0; // essential: w_0 = 0
b[0] = 0.0;
break;
case Support::Free: {
// Shear: (EI w'')'(0) = V_L, one-sided 2nd-order in the moment field
// (-3 m_0 + 4 m_1 - m_2)/(2h) = V_L, with m_0 = M_L known.
add_moment(0, 1, 4.0 / (2.0 * h));
add_moment(0, 2, -1.0 / (2.0 * h));
b[0] += V_L + 3.0 * M_L / (2.0 * h);
break;
}
}
// --- Right boundary row (row N).
switch (Rsup) {
case Support::Clamped:
case Support::Pinned:
A(N, N) = 1.0;
b[N] = 0.0;
break;
case Support::Free: {
// Shear: (EI w'')'(L) = V_R, one-sided 2nd-order in the moment field
// (3 m_N - 4 m_{N-1} + m_{N-2})/(2h) = V_R, with m_N = M_R known.
add_moment(N, N - 1, -4.0 / (2.0 * h));
add_moment(N, N - 2, 1.0 / (2.0 * h));
b[N] += V_R - 3.0 * M_R / (2.0 * h);
break;
}
}
return sys;
}
BeamResult BeamSolver::solve() const {
beam_.validate(); // propagate mechanism / ill-posed configuration errors
BeamSystem sys = assemble_system();
BeamResult result;
result.deflection = solve_general(sys.A, sys.b); // propagate singular-system error
return result;
}Build and run tests
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 -20
[ 11%] Building CXX object CMakeFiles/beamfd.dir/src/linalg.cpp.o
[ 22%] Building CXX object CMakeFiles/beamfd.dir/src/solver.cpp.o
[ 33%] Building CXX object CMakeFiles/beamfd.dir/src/io.cpp.o
[ 44%] Building CXX object CMakeFiles/beamfd.dir/src/beam.cpp.o
[ 55%] Linking CXX static library libbeamfd.a
[ 55%] Built target beamfd
[ 77%] Building CXX object CMakeFiles/beamfd_cli.dir/src/main.cpp.o
[ 77%] Building CXX object tests/CMakeFiles/test_smoke.dir/test_smoke.cpp.o
[ 88%] Linking CXX executable beamfd_cli
[ 88%] Built target beamfd_cli
[100%] Linking CXX executable test_smoke
[100%] Built target test_smoke
Test project /opt/beamfd/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) = 0.01 sec
[stdout]
[ 11%] Building CXX object CMakeFiles/beamfd.dir/src/linalg.cpp.o
[ 22%] Building CXX object CMakeFiles/beamfd.dir/src/solver.cpp.o
[ 33%] Building CXX object CMakeFiles/beamfd.dir/src/io.cpp.o
[ 44%] Building CXX object CMakeFiles/beamfd.dir/src/beam.cpp.o
[ 55%] Linking CXX static library libbeamfd.a
[ 55%] Built target beamfd
[ 77%] Building CXX object CMakeFiles/beamfd_cli.dir/src/main.cpp.o
[ 77%] Building CXX object tests/CMakeFiles/test_smoke.dir/test_smoke.cpp.o
[ 88%] Linking CXX executable beamfd_cli
[ 88%] Built target beamfd_cli
[100%] Linking CXX executable test_smoke
[100%] Built target test_smoke
Test project /opt/beamfd/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) = 0.01 secBuild and run manufactured-solution convergence checks
cat > /tmp/verify.cpp <<'EOF'
#include <cmath>
#include <cstdio>
#include <vector>
#include "beamfd/beam.hpp"
#include "beamfd/solver.hpp"
using namespace beamfd;
double maxerr(const std::vector<double>& w, const std::vector<double>& exact){
double e=0; for(size_t i=0;i<w.size();++i) e=std::max(e,std::fabs(w[i]-exact[i])); return e;
}
// Convergence helper: returns max error for given N
template<class Setup>
void conv(const char* name, Setup setup){
printf("%-40s ", name);
double prev=0;
for(int N : {20,40,80,160}){
auto pr = setup(N);
Beam& beam = *pr.first; auto exact = pr.second;
BeamSolver s(beam);
auto r = s.solve();
double e = maxerr(r.deflection, exact);
double rate = prev>0 ? std::log2(prev/e) : 0.0;
printf("N=%d e=%.3e", N, e);
if(prev>0) printf("(rate %.2f) ", rate); else printf(" ");
prev=e; delete pr.first;
}
printf("\n");
}
int main(){
double L=3.0;
// 1. pinned-pinned UDL
conv("pinned-pinned UDL", [&](int N){
auto* b=new Beam(L, 1000.0, N, Support::Pinned, Support::Pinned);
b->set_distributed_load(5.0);
std::vector<double> ex(b->num_nodes());
double q=5,EI=1000;
for(size_t i=0;i<ex.size();++i){double x=b->node_x(i); ex[i]=q/(24*EI)*(x*x*x*x-2*L*x*x*x+L*L*L*x);}
return std::make_pair(b,ex);
});
// 2. cantilever clamped-free tip load
conv("cantilever tip load", [&](int N){
double EI=2e6,P=1000;
auto* b=new Beam(L, EI, N, Support::Clamped, Support::Free);
b->set_end_load(P,false);
std::vector<double> ex(b->num_nodes());
for(size_t i=0;i<ex.size();++i){double x=b->node_x(i); ex[i]=P/(6*EI)*(3*L*x*x-x*x*x);}
return std::make_pair(b,ex);
});
// 3. clamped-clamped UDL
conv("clamped-clamped UDL", [&](int N){
double EI=1500,q=8;
auto* b=new Beam(L, EI, N, Support::Clamped, Support::Clamped);
b->set_distributed_load(q);
std::vector<double> ex(b->num_nodes());
for(size_t i=0;i<ex.size();++i){double x=b->node_x(i); ex[i]=q/(24*EI)*x*x*(L-x)*(L-x);}
return std::make_pair(b,ex);
});
// 4. variable EI (linear) + foundation, manufactured w=x^2(L-x)^2, clamped-clamped
conv("var-EI + foundation (manufactured)", [&](int N){
double a=1000.0,bb=300.0,k=50.0;
auto* beam=new Beam(L, a, N, Support::Clamped, Support::Clamped);
size_t n=beam->num_nodes();
std::vector<double> ei(n),kk(n),q(n),ex(n);
for(size_t i=0;i<n;++i){double x=beam->node_x(i);
ei[i]=a+bb*x; kk[i]=k;
double w=x*x*(L-x)*(L-x);
q[i]=24*a-24*bb*L+72*bb*x + k*w;
ex[i]=w;
}
beam->set_ei_nodal(ei); beam->set_foundation_nodal(kk); beam->set_q_nodal(q);
return std::make_pair(beam,ex);
});
// 5. free-free on foundation, manufactured. Need w with M,V=0 at ends (no applied).
// Use constant EI, k; choose w=cos? Instead set applied end actions from exact.
return 0;
}
EOF
cd /opt/beamfd && g++ -std=c++17 -I include /tmp/verify.cpp src/beam.cpp src/solver.cpp src/linalg.cpp -O2 -o /tmp/verify && /tmp/verifypinned-pinned UDL N=20 e=1.055e-05 N=40 e=2.637e-06(rate 2.00) N=80 e=6.592e-07(rate 2.00) N=160 e=1.648e-07(rate 2.00) cantilever tip load N=20 e=5.625e-06 N=40 e=1.406e-06(rate 2.00) N=80 e=3.516e-07(rate 2.00) N=160 e=8.811e-08(rate 2.00) clamped-clamped UDL N=20 e=2.250e-05 N=40 e=5.625e-06(rate 2.00) N=80 e=1.406e-06(rate 2.00) N=160 e=3.516e-07(rate 2.00) var-EI + foundation (manufactured) N=20 e=1.006e-01 N=40 e=2.515e-02(rate 2.00) N=80 e=6.288e-03(rate 2.00) N=160 e=1.572e-03(rate 2.00) [stdout] pinned-pinned UDL N=20 e=1.055e-05 N=40 e=2.637e-06(rate 2.00) N=80 e=6.592e-07(rate 2.00) N=160 e=1.648e-07(rate 2.00) cantilever tip load N=20 e=5.625e-06 N=40 e=1.406e-06(rate 2.00) N=80 e=3.516e-07(rate 2.00) N=160 e=8.811e-08(rate 2.00) clamped-clamped UDL N=20 e=2.250e-05 N=40 e=5.625e-06(rate 2.00) N=80 e=1.406e-06(rate 2.00) N=160 e=3.516e-07(rate 2.00) var-EI + foundation (manufactured) N=20 e=1.006e-01 N=40 e=2.515e-02(rate 2.00) N=80 e=6.288e-03(rate 2.00) N=160 e=1.572e-03(rate 2.00)
Verify free ends with applied actions, manufactured
cat > /tmp/verify2.cpp <<'EOF'
#include <cmath>
#include <cstdio>
#include <vector>
#include "beamfd/beam.hpp"
#include "beamfd/solver.hpp"
using namespace beamfd;
double maxerr(const std::vector<double>& w, const std::vector<double>& e){double m=0;for(size_t i=0;i<w.size();++i)m=std::max(m,std::fabs(w[i]-e[i]));return m;}
int main(){
double L=3.0;
// free-free on foundation, manufactured w=x^2(L-x)^2, const EI, const k
printf("free-free on foundation (manufactured), const EI/k:\n ");
double prev=0;
for(int N:{20,40,80,160}){
double E0=1000.0,k=40.0;
Beam beam(L,E0,N,Support::Free,Support::Free);
size_t n=beam.num_nodes();
std::vector<double> kk(n),q(n),ex(n);
for(size_t i=0;i<n;++i){double x=beam.node_x(i);double w=x*x*(L-x)*(L-x);
kk[i]=k; q[i]=24*E0+k*w; ex[i]=w;}
beam.set_foundation_nodal(kk); beam.set_q_nodal(q);
// end actions: M(0)=M(L)=E0*2L^2; V(0)=E0*(-12L); V(L)=E0*12L
beam.set_end_moment(E0*2*L*L,true); beam.set_end_moment(E0*2*L*L,false);
beam.set_end_load(-(E0*(-12*L)),true); // applied_end_shear=-P=V_L
beam.set_end_load(-(E0*(12*L)),false);
BeamSolver s(beam); auto r=s.solve();
double e=maxerr(r.deflection,ex);
printf("N=%d e=%.3e%s ",N,e, prev>0?(std::string("(rate ")+std::to_string(std::log2(prev/e))+")").c_str():"");
prev=e;
}
printf("\n");
// pinned-free on foundation, manufactured w=x^2(L-x)^2 (w(0)=0 ok pinned; M(0)=E0*2L^2!=0)
// pinned requires M=0 at that end -> need w''(0)=0. Choose w = sin-like? Use w=x^2(L-x)^3?
// Let's pick w with w(0)=0,w''(0)=0 (pinned at left), free at right. w=x(L-x)^2*(something)...
// Use w = x^3 ... simpler: w = (x)(L-x)(x-2L)?? Let's choose w=sin(pi x/L)? not polynomial.
// Use cubic-friendly: w = x^2*(L-x), then w''=2L-6x, w''(0)=2L!=0.
// w=x^3(L-x): w'=3x^2 L? compute w''=6Lx-12x^2, w''(0)=0 good (pinned left).
// free right: M(L)=E0 w''(L)=E0(6L^2-12L^2)=-6E0L^2; V=(E0w'')'=E0(6L-24x);V(L)=E0(6L-24L)=-18E0L
printf("pinned-free on foundation (manufactured):\n ");
prev=0;
for(int N:{20,40,80,160}){
double E0=1200.0,k=30.0;
Beam beam(L,E0,N,Support::Pinned,Support::Free);
size_t n=beam.num_nodes();
std::vector<double> kk(n),q(n),ex(n);
// w=x^3(L-x)=L x^3 - x^4; w''=6Lx-12x^2; w''''=-24; (E0w'')''=E0*(-24)
for(size_t i=0;i<n;++i){double x=beam.node_x(i);double w=L*x*x*x-x*x*x*x;
kk[i]=k; q[i]=-24*E0+k*w; ex[i]=w;}
beam.set_foundation_nodal(kk); beam.set_q_nodal(q);
beam.set_end_moment(E0*(-6*L*L),false); // M(L)
beam.set_end_load(-(E0*(-18*L)),false); // V(L)=-18E0L -> P=-V
BeamSolver s(beam); auto r=s.solve();
double e=maxerr(r.deflection,ex);
printf("N=%d e=%.3e%s ",N,e, prev>0?(std::string("(rate ")+std::to_string(std::log2(prev/e))+")").c_str():"");
prev=e;
}
printf("\n");
return 0;
}
EOF
g++ -std=c++17 -I include /tmp/verify2.cpp src/beam.cpp src/solver.cpp src/linalg.cpp -O2 -o /tmp/verify2 && /tmp/verify2free-free on foundation (manufactured), const EI/k: N=20 e=3.396e-02 N=40 e=8.415e-03(rate 2.012751) N=80 e=2.099e-03(rate 2.003304) N=160 e=5.250e-04(rate 1.999391) pinned-free on foundation (manufactured): N=20 e=5.097e-02 N=40 e=1.261e-02(rate 2.015350) N=80 e=3.143e-03(rate 2.003918) N=160 e=7.873e-04(rate 1.997246) [stdout] free-free on foundation (manufactured), const EI/k: N=20 e=3.396e-02 N=40 e=8.415e-03(rate 2.012751) N=80 e=2.099e-03(rate 2.003304) N=160 e=5.250e-04(rate 1.999391) pinned-free on foundation (manufactured): N=20 e=5.097e-02 N=40 e=1.261e-02(rate 2.015350) N=80 e=3.143e-03(rate 2.003918) N=160 e=7.873e-04(rate 1.997246)
Variable EI cantilever and mechanism detection
cat > /tmp/verify3.cpp <<'EOF'
#include <cmath>
#include <cstdio>
#include <vector>
#include "beamfd/beam.hpp"
#include "beamfd/solver.hpp"
using namespace beamfd;
double maxerr(const std::vector<double>& w,const std::vector<double>& e){double m=0;for(size_t i=0;i<w.size();++i)m=std::max(m,std::fabs(w[i]-e[i]));return m;}
int main(){
double L=3.0;
printf("clamped-free, VARIABLE EI=a+bx, manufactured w=x^2(L-x)^2:\n ");
double prev=0;
for(int N:{20,40,80,160,320}){
double a=1000.0,bb=400.0;
Beam beam(L,a,N,Support::Clamped,Support::Free);
size_t n=beam.num_nodes();
std::vector<double> ei(n),q(n),ex(n);
for(size_t i=0;i<n;++i){double x=beam.node_x(i);
ei[i]=a+bb*x; ex[i]=x*x*(L-x)*(L-x);
q[i]=24*a-24*bb*L+72*bb*x;}
beam.set_ei_nodal(ei); beam.set_q_nodal(q);
// right free: M(L)=(a+bL)*2L^2 ; V(L)=a*12L + b*14L^2
beam.set_end_moment((a+bb*L)*2*L*L,false);
double VL=a*12*L+bb*14*L*L;
beam.set_end_load(-VL,false); // applied_end_shear=-P=V
BeamSolver s(beam); auto r=s.solve();
double e=maxerr(r.deflection,ex);
printf("N=%d e=%.3e%s ",N,e,prev>0?(std::string("(rate ")+std::to_string(std::log2(prev/e))+")").c_str():"");
prev=e;
}
printf("\n");
// Also: singular detection , free-free no foundation should throw at validate
try{ Beam beam(L,1000,20,Support::Free,Support::Free); BeamSolver s(beam); s.solve();
printf("ERROR: free-free no foundation did not throw\n"); }
catch(const std::exception& e){ printf("free-free no foundation correctly threw: %s\n", e.what()); }
return 0;
}
EOF
g++ -std=c++17 -I include /tmp/verify3.cpp src/beam.cpp src/solver.cpp src/linalg.cpp -O2 -o /tmp/verify3 && /tmp/verify3clamped-free, VARIABLE EI=a+bx, manufactured w=x^2(L-x)^2: N=20 e=1.341e+00 N=40 e=3.345e-01(rate 2.003139) N=80 e=8.357e-02(rate 2.000786) N=160 e=2.089e-02(rate 2.000197) N=320 e=5.223e-03(rate 1.999984) free-free no foundation correctly threw: Beam::validate: free-free beam is a mechanism [stdout] clamped-free, VARIABLE EI=a+bx, manufactured w=x^2(L-x)^2: N=20 e=1.341e+00 N=40 e=3.345e-01(rate 2.003139) N=80 e=8.357e-02(rate 2.000786) N=160 e=2.089e-02(rate 2.000197) N=320 e=5.223e-03(rate 1.999984) free-free no foundation correctly threw: Beam::validate: free-free beam is a mechanism
Run demo CLI on example beam
./build/beamfd_cli examples/cantilever_tip.beam 2>&1 | tail -20; rm -f /tmp/verify*.cpp /tmp/verify /tmp/verify2 /tmp/verify3
181 2.715000e+00 3.860730e-03 2.850000e+02 -1.000000e+03 182 2.730000e+00 3.894191e-03 2.700000e+02 -1.000000e+03 183 2.745000e+00 3.927683e-03 2.550000e+02 -1.000000e+03 184 2.760000e+00 3.961204e-03 2.400000e+02 -1.000000e+03 185 2.775000e+00 3.994751e-03 2.250000e+02 -1.000000e+03 186 2.790000e+00 4.028324e-03 2.100000e+02 -1.000000e+03 187 2.805000e+00 4.061920e-03 1.950000e+02 -1.000000e+03 188 2.820000e+00 4.095539e-03 1.800000e+02 -1.000000e+03 189 2.835000e+00 4.129177e-03 1.650000e+02 -1.000000e+03 190 2.850000e+00 4.162835e-03 1.500000e+02 -1.000000e+03 191 2.865000e+00 4.196509e-03 1.350000e+02 -1.000000e+03 192 2.880000e+00 4.230198e-03 1.200000e+02 -1.000000e+03 193 2.895000e+00 4.263901e-03 1.050000e+02 -1.000000e+03 194 2.910000e+00 4.297615e-03 9.000000e+01 -1.000000e+03 195 2.925000e+00 4.331340e-03 7.500000e+01 -1.000000e+03 196 2.940000e+00 4.365073e-03 6.000000e+01 -1.000000e+03 197 2.955000e+00 4.398813e-03 4.500000e+01 -1.000000e+03 198 2.970000e+00 4.432558e-03 3.000000e+01 -1.000000e+03 199 2.985000e+00 4.466306e-03 1.500000e+01 -1.000000e+03 200 3.000000e+00 4.500056e-03 7.709882e-09 -1.000000e+03 [stdout] 181 2.715000e+00 3.860730e-03 2.850000e+02 -1.000000e+03 182 2.730000e+00 3.894191e-03 2.700000e+02 -1.000000e+03 183 2.745000e+00 3.927683e-03 2.550000e+02 -1.000000e+03 184 2.760000e+00 3.961204e-03 2.400000e+02 -1.000000e+03 185 2.775000e+00 3.994751e-03 2.250000e+02 -1.000000e+03 186 2.790000e+00 4.028324e-03 2.100000e+02 -1.000000e+03 187 2.805000e+00 4.061920e-03 1.950000e+02 -1.000000e+03 188 2.820000e+00 4.095539e-03 1.800000e+02 -1.000000e+03 189 2.835000e+00 4.129177e-03 1.650000e+02 -1.000000e+03 190 2.850000e+00 4.162835e-03 1.500000e+02 -1.000000e+03 191 2.865000e+00 4.196509e-03 1.350000e+02 -1.000000e+03 192 2.880000e+00 4.230198e-03 1.200000e+02 -1.000000e+03 193 2.895000e+00 4.263901e-03 1.050000e+02 -1.000000e+03 194 2.910000e+00 4.297615e-03 9.000000e+01 -1.000000e+03 195 2.925000e+00 4.331340e-03 7.500000e+01 -1.000000e+03 196 2.940000e+00 4.365073e-03 6.000000e+01 -1.000000e+03 197 2.955000e+00 4.398813e-03 4.500000e+01 -1.000000e+03 198 2.970000e+00 4.432558e-03 3.000000e+01 -1.000000e+03 199 2.985000e+00 4.466306e-03 1.500000e+01 -1.000000e+03 200 3.000000e+00 4.500056e-03 7.709882e-09 -1.000000e+03
No file changes, the agent left the workspace untouched.
== 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.Q2asU4Ksnd/beamfd/build_grade
== Building ==
[ 6%] Building CXX object CMakeFiles/beamfd.dir/src/solver.cpp.o
[ 13%] Building CXX object CMakeFiles/beamfd.dir/src/beam.cpp.o
[ 20%] Building CXX object CMakeFiles/beamfd.dir/src/linalg.cpp.o
[ 26%] Building CXX object CMakeFiles/beamfd.dir/src/io.cpp.o
[ 33%] Linking CXX static library libbeamfd.a
[ 33%] Built target beamfd
[ 40%] Building CXX object CMakeFiles/beamfd_cli.dir/src/main.cpp.o
[ 46%] Building CXX object tests/CMakeFiles/test_mms.dir/test_mms.cpp.o
[ 53%] Building CXX object tests/CMakeFiles/test_invariants.dir/test_invariants.cpp.o
[ 60%] Building CXX object tests/CMakeFiles/test_soak.dir/test_soak.cpp.o
[ 66%] Building CXX object tests/CMakeFiles/test_convergence.dir/test_convergence.cpp.o
[ 73%] Linking CXX executable beamfd_cli
[ 73%] Built target beamfd_cli
[ 80%] Linking CXX executable test_convergence
[ 93%] Linking CXX executable test_soak
[ 93%] Linking CXX executable test_invariants
[ 93%] Built target test_convergence
[100%] Linking CXX executable test_mms
[100%] Built target test_soak
[100%] Built target test_invariants
[100%] Built target test_mms
== Running hidden test suite (ctest) ==
Test project /tmp/tmp.Q2asU4Ksnd/beamfd/build_grade
Start 1: test_mms
1/4 Test #1: test_mms ......................... Passed 0.01 sec
Start 2: test_convergence
2/4 Test #2: test_convergence ................. Passed 0.00 sec
Start 3: test_invariants
3/4 Test #3: test_invariants .................. Passed 0.00 sec
Start 4: test_soak
4/4 Test #4: test_soak ........................ Passed 0.01 sec
100% tests passed, 0 tests failed out of 4
Label Time Summary:
hidden = 0.02 sec*proc (4 tests)
Total Test time (real) = 0.03 sec
PASS: all hidden tests passedReproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_adc72b3d4c0144de. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.
Trial trial_adc72b3d4c0144de · verifier authoritative; classifier explanatory.