Validation.

Problem. Steel bar 150 × 10 × 15 mm, clamped at one end, 200 N down on the other.

Reference. Beam theory with shear (Timoshenko) for the deflection; M·c/I for the stress, read 2.5 depths from the clamp.

• tip deflection: 0.382 mm against 0.384 mm, −0.54 % (tolerance ±2 %), within. Mesh: 41,090 elements, 1.382 mm.
• bending stress, top face, a quarter of the way along: 60 MPa against 60 MPa, +0.01 % (tolerance ±2 %), within. Mesh: 41,090 elements, 1.382 mm.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. Steel bar 120 × 10 × 10 mm, clamped at one end, pulled with 20 kN at the other.

Reference. F·L / (A·E), exact.

• elongation: 0.114 mm against 0.114 mm, −0.26 % (tolerance ±2 %), within. Mesh: 41,165 elements, 1.121 mm.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. Plate 80 × 240 × 2 mm with a 10 mm hole, pulled at 50 MPa; a quarter of it, held on its two symmetry planes.

Reference. Heywood’s formula for the stress concentration factor, Kt = (2 + (1 − d/W)³) / (1 − d/W).

• stress concentration factor Kt at the hole: 3.135 against 3.051, +2.74 % (tolerance ±3 %), within. Mesh: 52,809 elements, 1.039 mm.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. Tube with a 20 mm bore, 40 mm outside, 20 mm long, 100 MPa on the bore; a quarter of it, held on its two side symmetry planes.

Reference. Lamé’s solution for a thick cylinder with open ends, exact.

• hoop stress at the bore: no number against 166.7 MPa (tolerance ±2 %), no result. Refused: with a pressure on a curved face and only side symmetry planes held, the check calls the part free to move and gives no number. The same tube with one more plane held, below, solves.
• radial growth of the bore: no number against 0.00937 mm (tolerance ±2 %), no result. Refused with the row above: no number.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. The same tube, with its mid-length symmetry plane held as well. The exact answer does not change.

Reference. Lamé’s solution for a thick cylinder with open ends, exact.

• hoop stress at the bore: 166 MPa against 166.7 MPa, −0.37 % (tolerance ±2 %), within. Mesh: 42,986 elements, 0.821 mm.
• radial growth of the bore: 0.00935 mm against 0.00937 mm, −0.15 % (tolerance ±2 %), within. Mesh: 42,986 elements, 0.821 mm.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. Steel column 200 × 8 × 8 mm, fixed at the base, free at the top, pushed down along its axis.

Reference. Euler’s critical load for a fixed–free column, π²EI / (2L)².

• critical load: 4,424 N against 4,422 N, +0.06 % (tolerance ±2 %), within. Mesh: 33,369 elements.

Measured on our test server. On the live site a buckling solve has not yet finished in our own checks, so buckling is not yet offered as proven.

Open this case in MeshWeave Opens the part with this set-up; press Buckling to solve it. Needs the engineering tools.

Problem. Steel bar 200 × 10 × 10 mm, clamped at one end.

Reference. Euler–Bernoulli beam, first bending mode (βL = 1.8751).

• first bending frequency: 209 Hz against 208.9 Hz, +0.04 % (tolerance ±2 %), within. Mesh: 41,631 elements.

Open this case in MeshWeave Opens the part with this set-up; press Frequencies to solve it. Needs the engineering tools.

Problem. Steel bar 300 × 10 × 10 mm, clamped at both ends.

Reference. Euler–Bernoulli beam, first and second bending modes (βL = 4.7300 and 7.8532).

• first bending frequency: 588.2 Hz against 590.7 Hz, −0.43 % (tolerance ±2 %), within. Mesh: 42,495 elements.
• second bending frequency: 1,606 Hz against 1,628 Hz, −1.39 % (tolerance ±2 %), within. Mesh: 42,495 elements.

Open this case in MeshWeave Opens the part with this set-up; press Frequencies to solve it. Needs the engineering tools.

Problem. Steel bar 100 × 20 × 20 mm with insulated sides, one end at 100 °C and the other at 0 °C.

Reference. One-dimensional conduction: a straight-line profile, exact.

• temperature a quarter of the way along: 75 °C against 75 °C, +0.00 % (tolerance ±1 %), within. Mesh: 63,547 elements, 1.442 mm.

Open this case in MeshWeave Opens the part with this set-up; press Thermal to solve it. Needs the engineering tools.

Problem. The same bar, 10 W into one end and the other end held at 20 °C.

Reference. T₀ + QL/kA, exact.

• temperature of the heated end: 70 °C against 70 °C, −0.00 % (tolerance ±1 %), within. Mesh: 63,547 elements, 1.442 mm.

Open this case in MeshWeave Opens the part with this set-up; press Thermal to solve it. Needs the engineering tools.

Problem. The same bar, 10 W into one end and the other end cooled by air at 20 °C (500 W/m²K).

Reference. T∞ + Q(1/hA + L/kA), exact.

• temperature of the heated end: 120 °C against 120 °C, −0.00 % (tolerance ±1 %), within. Mesh: 63,547 elements, 1.442 mm.

Open this case in MeshWeave Opens the part with this set-up; press Thermal to solve it. Needs the engineering tools.

Problem. The same bar with 10 W in and the far end cooled, the two ends picked as faces in the editor rather than marked by a box.

Reference. T∞ + Q(1/hA + L/kA), exact.

• heated-end temperature: 120 °C against 120 °C, −0.00 % (tolerance ±1 %), within. Mesh: 63,547 elements, 1.442 mm.

Open this case in MeshWeave Opens the part with this set-up; press Thermal to solve it. Needs the engineering tools.

Problem. A quarter of an elliptic ring 100 mm thick, 10 MPa outward on its outer edge, held on its symmetry planes.

Reference. The published target value of the NAFEMS benchmark LE1.

• stress σyy at point D: 93.51 MPa against 92.7 MPa, +0.87 % (tolerance ±2 %), within. Mesh: 45,219 elements, 39.99 mm.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. A quarter of an elliptic plate 600 mm thick, 1 MPa on its top face, its outer edge held and a mid-thickness line fixed.

Reference. The published target value of the NAFEMS benchmark LE10.

• stress σyy at point D, top face: -5.386 MPa against -5.38 MPa, −0.12 % (tolerance ±3 %), within. Mesh: 45,668 elements, 72.66 mm.

Open this case in MeshWeave Opens the part with this set-up; press Strength to solve it. Needs the engineering tools.

Problem. A 10 m tapered plate 50 mm thick of 316L steel, clamped along its wide end, vibrating in its own plane.

Reference. The published target value of the NAFEMS benchmark FV32 (its first six in-plane modes).

• in-plane mode 1: 44.63 Hz against 44.62 Hz, +0.02 % (tolerance ±2 %), within. Mesh: 58,769 elements.
• in-plane mode 2: 130 Hz against 130 Hz, +0.00 % (tolerance ±2 %), within. Mesh: 58,769 elements.
• in-plane mode 3: 162.7 Hz against 162.7 Hz, +0.02 % (tolerance ±2 %), within. Mesh: 58,769 elements.
• in-plane mode 4: 246 Hz against 246.1 Hz, −0.02 % (tolerance ±2 %), within. Mesh: 58,769 elements.
• in-plane mode 5: 379.7 Hz against 379.9 Hz, −0.04 % (tolerance ±2 %), within. Mesh: 58,769 elements.
• in-plane mode 6: 391.5 Hz against 391.4 Hz, +0.02 % (tolerance ±2 %), within. Mesh: 58,769 elements.

Open this case in MeshWeave Opens the part with this set-up; press Frequencies to solve it. Needs the engineering tools.

Problem. A 600 × 1000 mm plate: one edge at 100 °C, two edges cooled by air at 0 °C, one insulated.

Reference. The published target value of the NAFEMS benchmark T4, at its own Biot number.

• temperature at point E: 18.26 °C against 18.25 °C, +0.06 % (tolerance ±2 %), within. Mesh: 65,171 elements, 16.51 mm.

Open this case in MeshWeave Opens the part with this set-up; press Thermal to solve it. Needs the engineering tools.

Problem. A plate with a heated region in its middle: the stress the heat alone causes.

Reference. The published target value of the NAFEMS benchmark T1.

• stress σyy at point D: no number against 50 MPa (tolerance ±2 %), no result. Not supported yet: a strength check cannot take a temperature load (thermal strain), so this case cannot be set up.