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Verification gallery

58 verification problems, solved mesh-free.

Static, modal, thermal, nonlinear, dynamics and composite problems from the SimSolid Verification Manual. Each was rebuilt from its stated dimensions, solved with Naksha's mesh-free solver and compared with its reference solution.

58problems solved
0.8%median worst-result deviation
39within 2% of the reference
52within 5% of the reference
Head to head

Naksha against SimSolid's published results

On the 56 problems where both have a value, we compare the mean |Δ| from the reference across all of each problem's results. A difference under 0.1 percentage points counts as a tie.

SimSolid values are as published by Altair in the SimSolid Verification Manual (retrieved 15 October 2026), and the SimSolid version isn't stated there. Naksha's models were built independently from each problem's stated dimensions, so part of any difference can come from modelling choices rather than the solver.

31Naksha closer
16SimSolid closer
9tie
VS01Static−0.8%worst result
VS01SS-V 1000−0.8%

Straight Cantilever Beam

Tie: equally close to the reference mean |Δ| Naksha 0.39% · SimSolid 0.45%

Reference: MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1…

QuantityReferenceNakshaΔSimSolid
Axial Loading (+X direction) [in]3×10-53×10-5−0.1%+0.1%
In-plane Shear (+Y direction) [in]0.10810.1078−0.3%+0.1%
Out-of-plane Shear (+Z direction) [in]0.43210.4306−0.4%+0.1%
Twisting* (+Z direction) [in]0.0034060.003378−0.8%+1.5%
VS02Static−0.6%worst result
VS02SS-V 1010−0.6%

Twisted Cantilever Beam

Naksha closer to the reference mean |Δ| Naksha 0.44% · SimSolid 3.84%

Reference: MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1…

QuantityReferenceNakshaΔSimSolid
In-plane Shear (+Y direction) [in]0.0054240.005392−0.6%+0.6%
Out-of-plane Shear (+ X direction) [in]0.0017540.001749−0.3%−7.1%
VS03Static+1.2%worst result
VS03SS-V 1020+1.2%

Curved Beam

SimSolid closer to the reference mean |Δ| Naksha 1.16% · SimSolid 1.02%

Reference: MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1…

QuantityReferenceNakshaΔSimSolid
In-plane Load (+Y direction) [in]0.087340.08839+1.2%+1.4%
Out-of-plane Load (+ Z direction) [in]0.50220.4966−1.1%+0.6%
VS04Static+0.3%worst result
VS04SS-V 1030+0.3%

Simply Supported Thin Plate

Tie: equally close to the reference mean |Δ| Naksha 0.21% · SimSolid 0.15%

Reference: MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1…

QuantityReferenceNakshaΔSimSolid
Uniform load [in]4.06×10-64.07×10-6+0.3%+0.2%
Point load [in]1.16×10-51.16×10-5+0.2%+0.1%
VS05Static−0.1%worst result
VS05SS-V 1040−0.1%

Clamped Thin Plate

Naksha closer to the reference mean |Δ| Naksha 0.07% · SimSolid 0.42%

Reference: MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1…

QuantityReferenceNakshaΔSimSolid
Uniform load [in]1.26×10-61.26×10-60.0%+0.7%
Point load [in]5.6×10-65.59×10-6−0.1%+0.2%
VS06Static+1.5%worst result
VS06SS-V 1050+1.5%

Tapered Solid Bar

SimSolid closer to the reference mean |Δ| Naksha 0.89% · SimSolid 0.42%

Reference: Harris, C.O., Introduction to Stress Analysis, The MacMillan Co., New York, 1959, pp. 237, Problem 4.

QuantityReferenceNakshaΔSimSolid
Maximum Axial Deflection [in] [in]0.0048080.00482+0.2%+0.5%
Axial Stress* at Midpoint [psi] [psi]44444512+1.5%−0.4%
VS07Static+2.2%worst result
VS07SS-V 1060+2.2%

Cantilever Plate

SimSolid closer to the reference mean |Δ| Naksha 2.16% · SimSolid 1.91%

Reference: Ferdinand L., Singer, Strength of Materials, (Harper & Row, 1962), Art. 52, p. 133.

QuantityReferenceNakshaΔSimSolid
Maximum Bending Stress (psi) [psi]6e+046.13e+04+2.2%+1.9%
VS08Static+2.2%worst result
VS08SS-V 1070+2.2%

Plate with a Hole

SimSolid closer to the reference mean |Δ| Naksha 2.22% · SimSolid 1.28%

Reference: No literature footnote on the page. Reference formula given on the page: sigma_max = k sigma_nom; sigma_nom = F h/(h - r) = 166,7 MPa; k = 3 -…

QuantityReferenceNakshaΔSimSolid
Maximum Stress [MPa] [MPa]372.7381+2.2%+1.3%
VS09Static−0.3%worst result
VS09SS-V 1080−0.3%

Scordelis-Lo Roof

Naksha closer to the reference mean |Δ| Naksha 0.29% · SimSolid 0.77%

Reference: No literature footnote on the page; the problem is the MacNeal-Harder (1985) Scordelis-Lo roof. Page: 'The theoretical solution value of the Z…

QuantityReferenceNakshaΔSimSolid
Maximum Z Displacement [m] [m]0.30860.3077−0.3%+0.8%
VS11Static−2.3%worst result
VS11SS-V 1100−2.3%

Raasch Challenge

SimSolid closer to the reference mean |Δ| Naksha 2.32% · SimSolid 0.08%

Reference: F.T. Wong, Testing of Shell Elements using Challenging Benchmark Problems.

QuantityReferenceNakshaΔSimSolid
Tip displacement [in]4.9364.821−2.3%−0.1%
VS13Static+0.3%worst result
VS13SS-V 1120+0.3%

Simply Supported Beam with Mid-span Load

Naksha closer to the reference mean |Δ| Naksha 0.18% · SimSolid 0.32%

Reference: No literature footnote. Page formulas: delta_max = F L^3/(48 E I), I = b h^3/12; sigma_max = F L/(4 Z), Z = b h^2/6 (the numeric values after '='…

QuantityReferenceNakshaΔSimSolid
Max Displacement [mm] [mm]1.0711.074+0.3%+0.5%
Max Stress [MPa] [MPa]150149.9−0.1%−0.2%
VS14Static+1.6%worst result
VS14SS-V 1130+1.6%

Skew Plate Under Pressure

Naksha closer to the reference mean |Δ| Naksha 1.64% · SimSolid 2.53%

Reference: Page: 'The reference solution is from analytical solution for thin plate formation.' The problem is NAFEMS LE6 (Skew plate under normal pressure,…

QuantityReferenceNakshaΔSimSolid
Maximum Principle Stress [MPa] [MPa]0.8020.8151+1.6%+2.5%
VS16Static · buckling+0.3%worst result
VS16SS-V 1150+0.3%

Buckling

SimSolid closer to the reference mean |Δ| Naksha 0.26% · SimSolid 0.12%

Reference: James M. Gere, Mechanics of Materials, 6th Edition. Page formula: P_cr = pi^2 E I / (K L)^2, K = effective length factor = 2 for cantilever beam.

QuantityReferenceNakshaΔSimSolid
Critical Load [kN]6.96.918+0.3%+0.1%
VS21Static+1.2%worst result
VS21SS-V 1200+1.2%

Tangential Edge Stress in an Elliptic Membrane

Naksha closer to the reference mean |Δ| Naksha 1.16% · SimSolid 1.55%

Reference: Test LE1 from NAFEMS Publication NNB, Rev. 3, NAFEMS Linear Benchmarks, 5 Oct 1990.

QuantityReferenceNakshaΔSimSolid
Tangential edge stress sigma_yy at D [MPa]92.793.77+1.2%−1.6%
VS22Static+0.9%worst result
VS22SS-V 1210+0.9%

Tangential Stress for a Cylindrical Shell

Naksha closer to the reference mean |Δ| Naksha 0.55% · SimSolid 1.75%

Reference: Test LE2 from NAFEMS Publication NNB, Rev. 3, NAFEMS Linear Benchmarks, 5 Oct 1990.

QuantityReferenceNakshaΔSimSolid
Case 1 [MPa]6059.87−0.2%−1.3%
Case 2 [MPa]6060.53+0.9%−2.2%
VS23Static−3.2%worst result
VS23SS-V 1220−3.2%

Displacements in Hemispherical Shell

SimSolid closer to the reference mean |Δ| Naksha 3.20% · SimSolid 0.49%

Reference: Test LE3 from NAFEMS Publication NNB, Rev. 3, NAFEMS Linear Benchmarks, 5 Oct 1990.

QuantityReferenceNakshaΔSimSolid
Displacement at A along x-axis [m]0.1850.1791−3.2%+0.5%
VM01Modal0.0%worst result
VM01SS-V 20000.0%

Free Vibration of a Wedge

Naksha closer to the reference mean |Δ| Naksha 0.01% · SimSolid 0.16%

Reference: Timoshenko, S., and Young, D.N., 'Vibration Problems in Engineering', 3rd Edition, D. Van Nostrand Co., Inc., New York, 1955, pg. 392, Art. 62.

QuantityReferenceNakshaΔSimSolid
Fundamental Frequency [Hz]259.2259.10.0%−0.2%
VM02Modal−0.2%worst result
VM02SS-V 2010−0.2%

In-plane Vibration of a Cantilever Plate

Naksha closer to the reference mean |Δ| Naksha 0.21% · SimSolid 1.01%

Reference: Roark, R.J. and Young, W.C., Formula for Stress and Strain, (New York:McGraw-Hill Book 6, 1982) pp. 576-578.

QuantityReferenceNakshaΔSimSolid
Fundamental Frequency [Hz]101.3101.1−0.2%−1.0%
VM03Modal−0.2%worst result
VM03SS-V 2020−0.2%

Cylindrical Shell

Naksha closer to the reference mean |Δ| Naksha 0.20% · SimSolid 0.77%

Reference: Roark, R.J. and Young, W.C., Formula for Stress and Strain, NY: McGraw-Hill Co. 1982, p.576

QuantityReferenceNakshaΔSimSolid
Fundamental Frequency [Hz]62.0561.93−0.2%−0.8%
VM04Modal+3.8%worst result
VM04SS-V 2030+3.8%

Free Thin Square Plate

SimSolid closer to the reference mean |Δ| Naksha 1.92% · SimSolid 0.22%

Reference: 1: The Standard NAFEMS Benchmarks TNSB, Rev. 3, 5 October, 1990. 2: Iguchi S. Biegeschwingungen and Klangfiguren der Vierseitg freien rechteckigen…

QuantityReferenceNakshaΔSimSolid
Flexible mode 1 [Hz]1.6221.6220.0%−0.2%
Flexible mode 2 [Hz]2.362.3590.0%−0.1%
Flexible mode 3 [Hz]2.9222.926+0.1%−0.1%
Flexible mode 4 [Hz]4.194.285+2.3%−0.3%
Flexible mode 5 [Hz]4.194.285+2.3%−0.3%
Flexible mode 6 [Hz]7.3567.605+3.4%−0.1%
Flexible mode 7 [Hz]7.3567.605+3.4%−0.1%
Flexible mode 8 [Hz]7.6687.963+3.8%−0.5%
Flexible mode 9 [Hz]—8.593——
Flexible mode 10 [Hz]—9.754——
Flexible mode 11 [Hz]—15.07——
Flexible mode 12 [Hz]—15.9——
Flexible mode 13 [Hz]—17.74——
Flexible mode 14 [Hz]—17.74——
VM05Modal+1.5%worst result
VM05SS-V 2040+1.5%

Thick Skewed Plate

SimSolid closer to the reference mean |Δ| Naksha 1.51% · SimSolid 0.84%

Reference: The Standard NAFEMS Benchmarks TNSB, Rev. 3, 5 October, 1990.

QuantityReferenceNakshaΔSimSolid
Fundamental Frequency [Hz]133.9136+1.5%+0.8%
VM06Modal+17.8%worst result
VM06SS-V 2050+17.8%

Thick Square Plate

SimSolid closer to the reference mean |Δ| Naksha 10.89% · SimSolid 1.51%

Reference: The Standard NAFEMS Benchmarks TNSB, Rev. 3, 5 October, 1990, Test No. FV 52

QuantityReferenceNakshaΔSimSolid
Mode 4 [Hz (not printed)]42.4744.61+5.0%+0.8%
Mode 5, 6 [Hz (not printed)]100.7112.7+11.9%+1.4%
Mode 7 [Hz (not printed)]147.9174.2+17.8%+2.1%
Mode 8 [Hz (not printed)]183.7212.5+15.7%+2.5%
Mode 9 [Hz (not printed)]185.4212.7+14.8%+2.2%
Mode 10 [Hz (not printed)]193.6194+0.2%−0.1%
VM08Modal−0.4%worst result
VM08SS-V 2070−0.4%

Cantilever Beam

Naksha closer to the reference mean |Δ| Naksha 0.23% · SimSolid 0.40%

Reference: NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis…

QuantityReferenceNakshaΔSimSolid
Mode 2 [Hz]6.3276.348+0.3%−0.1%
Mode 3 [Hz]17.7217.76+0.2%−0.2%
Mode 4 [Hz]34.7234.740.0%−0.4%
Mode 5 [Hz]57.3957.3−0.2%−0.6%
Mode 6 [Hz]85.7385.38−0.4%−0.8%
VM09Modal−2.1%worst result
VM09SS-V 2080−2.1%

Circular Ring - In-plane and Out-of-plane Vibration

Naksha closer to the reference mean |Δ| Naksha 1.18% · SimSolid 1.46%

Reference: NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis,…

QuantityReferenceNakshaΔSimSolid
Mode 7, 8 out-of-plane [Hz (not printed)]51.8551.51−0.7%−0.7%
Mode 9, 10 in-plane [Hz (not printed)]53.3853.19−0.4%−0.4%
Mode 11, 12 out-of-plane [Hz (not printed)]148.8146.8−1.3%−1.4%
Mode 13, 14 in-plane [Hz (not printed)]151149.6−0.9%−1.0%
Mode 15 out-of-plane [Hz (not printed)]287280.9−2.1%−2.2%
Mode 16 in-plane [Hz (not printed)]289.5284.6−1.7%−3.1%
VM10Modal+3.0%worst result
VM10SS-V 2090+3.0%

Triangular Wing - Fixed Vibration

SimSolid closer to the reference mean |Δ| Naksha 2.77% · SimSolid 0.59%

Reference: I.S. Tuba and W.B. Wright, ASME Pressure Vessel and Piping 1972 Computer Programs Verification, ASME publication, I-24, Problem 2

QuantityReferenceNakshaΔSimSolid
Mode 1 [Hz]55.957.34+2.6%−0.3%
Mode 2 [Hz]210.9216.7+2.7%−0.5%
Mode 3 [Hz]293.5302.3+3.0%−1.0%
VM11Modal+3.6%worst result
VM11SS-V 2100+3.6%

Cantilevered Tapered Beam

SimSolid closer to the reference mean |Δ| Naksha 1.26% · SimSolid 0.06%

Reference: NAFEMS R0015 - Selected benchmarks for natural frequency analysis.

QuantityReferenceNakshaΔSimSolid
Mode 1 [Hz (not printed)]44.6244.65+0.1%0.0%
Mode 2 [Hz (not printed)]130130.1+0.1%−0.1%
Mode 3 [Hz (not printed)]162.7162.70.0%0.0%
Mode 4 [Hz (not printed)]246.1247.8+0.7%−0.1%
Mode 5 [Hz (not printed)]379.9391.6+3.1%−0.1%
Mode 6 [Hz (not printed)]391.4405.6+3.6%0.0%
VM12Modal−0.4%worst result
VM12SS-V 2110−0.4%

Cantilever with Off-Center Remote Mass

Naksha closer to the reference mean |Δ| Naksha 0.17% · SimSolid 0.35%

Reference: Test FV4 from The Standard NAFEMS Benchmarks TNSB, Rev. 3, 5 October, 1990.

QuantityReferenceNakshaΔSimSolid
Mode 1 [Hz (not printed)]1.7231.725+0.1%−0.1%
Mode 2 [Hz (not printed)]1.7271.729+0.1%−0.1%
Mode 3 [Hz (not printed)]7.4137.407−0.1%−0.2%
Mode 4 [Hz (not printed)]9.9729.9740.0%−0.3%
Mode 5 [Hz (not printed)]18.1618.09−0.3%−0.7%
Mode 6 [Hz (not printed)]26.9626.86−0.4%−0.8%
VM13Modal · damped modal0.0%worst result
VM13SS-V 21200.0%

Two-body Symmetric Damped Oscillators System

Naksha closer to the reference mean |Δ| Naksha 0.00% · SimSolid 0.31%

Reference: Kausel E., 'Advanced Structural Dynamics', Cambridge University Press, 2017, Section 3: 'Multiple Degree of Freedom Systems' (general equations).

QuantityReferenceNakshaΔSimSolid
Mode 1 [Hz]0.1590.1590.0%−0.1%
Mode 1 [1/s]0.050.050.0%−0.5%
Mode 2 [Hz]0.21920.21920.0%+0.4%
Mode 2 [1/s]1.051.050.0%−0.2%
VM14Modal · damped modal0.0%worst result
VM14SS-V 21300.0%

1D Damped Oscillator: Translation or Rotation

Tie: equally close to the reference mean |Δ| Naksha 0.00% · SimSolid 0.00%

Reference: Kausel E., 'Advanced Structural Dynamics', Cambridge University Press, 2017, p.86.

QuantityReferenceNakshaΔSimSolid
Translation [Hz]1.4831.4830.0%0.0%
Translation [1/s]6.3696.3690.0%0.0%
Rotation [Hz]245.8245.80.0%0.0%
Rotation [1/s]229322930.0%0.0%
VT01Thermal0.0%worst result
VT01SS-V 30000.0%

Cooling fin

Naksha closer to the reference mean |Δ| Naksha 0.02% · SimSolid 1.26%

Reference: {"citation": "Kreith, F. Principles of Heat Transfer. 2nd ed. P.A.: International Textbook Co., 1959, pg. 48", "page_footnote": "*The reference…

QuantityReferenceNakshaΔSimSolid
Mean Temp at Insulated End [deg-F]68.5968.610.0%0.0%
Thermal Flux Through Heated End [BTU/(hr*in^2)]17.517.50.0%−2.5%
VT02Thermal+0.2%worst result
VT02SS-V 3010+0.2%

Insulated Wall

Naksha closer to the reference mean |Δ| Naksha 0.10% · SimSolid 0.24%

Reference: {"citation": "Kreith, F. Principles of Heat Transfer. 2nd ed. P.A.: International Textbook Co., 1959, pg. 32", "page_footnote": "*Reference…

QuantityReferenceNakshaΔSimSolid
Temp at Firebrick [deg-F]295729570.0%0.0%
Temp at Insulating Brick [deg-F]336336.7+0.2%+0.2%
Heat Flux Through Wall [BTU/(hr*ft^2)]513513.4+0.1%−0.5%
VT03Thermal−0.1%worst result
VT03SS-V 3020−0.1%

Cylinder with Prescribed Heat Flux

Naksha closer to the reference mean |Δ| Naksha 0.14% · SimSolid 1.36%

Reference: {"citation": "NAFEMS, BMTTA (S), No. 15 (i).", "related": "PTC Creo Simulate verification guide mvts003 '2D Axisymmetric Cylinder with Prescribed…

QuantityReferenceNakshaΔSimSolid
Temperature at Point A [deg-C]213.6213.3−0.1%−1.4%
VT04Thermal+0.3%worst result
VT04SS-V 3030+0.3%

Heat Generating Plate

Tie: equally close to the reference mean |Δ| Naksha 0.15% · SimSolid 0.17%

Reference: {"citation": "Kreith, F. Principles of Heat Transfer. 2nd ed. P.A.: International Textbook Co., 1959, pg. 42, ex. 2-9", "related": "ANSYS VM94…

QuantityReferenceNakshaΔSimSolid
Temperature at Mid-plane [deg-F]299.1300+0.3%+0.3%
Heat Flow Rate to Fluid [BTU/(hr*ft^2)]208320830.0%0.0%
VT05Thermal−0.1%worst result
VT05SS-V 3040−0.1%

Heat Generating Wire

Naksha closer to the reference mean |Δ| Naksha 0.08% · SimSolid 0.42%

Reference: W.M.Rohsenow, H.Y.Choi, Heat, Mass and Momentum Transfer, 2nd ed. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1963, pg. 106, ex. 6.5.

QuantityReferenceNakshaΔSimSolid
Temperature at Centerline [deg-F]419.9419.6−0.1%−0.4%
Temperature at Surface [deg-F]417.9417.5−0.1%−0.4%
VT06Thermal+0.8%worst result
VT06SS-V 3050+0.8%

Table Frame

Naksha closer to the reference mean |Δ| Naksha 0.46% · SimSolid 1.02%

Reference: {"citation": "LM-TH-1 Learning Module 1, Thermal Analysis, Dr. Jack Xin, Dr. Liang-Wu Cai, www.femlearning.org, 2010.", "availability":…

QuantityReferenceNakshaΔSimSolid
Temperature at A [deg C (unit not printed)]110.2110.9+0.6%+1.7%
Temperature at B [deg C (unit not printed)]182182.2+0.1%−0.8%
Temperature at C [deg C (unit not printed)]107.6108.4+0.8%+1.6%
Temperature at D [deg C (unit not printed)]143143.5+0.3%0.0%
VT07Thermal−20.0%worst result
VT07SS-V 3060−20.0%

Thermal

SimSolid closer to the reference mean |Δ| Naksha 20.03% · SimSolid 0.27%

Reference: {"citation": "NAFEMS, YARD report 3087 (Test 10)", "standard": "NAFEMS T4 'Two-dimensional heat transfer with convection', The Standard NAFEMS…

QuantityReferenceNakshaΔSimSolid
Temperature at point [C]18.314.63−20.0%−0.3%
VT08Thermal0.0%worst result
VT08SS-V 30700.0%

Transient Thermal

Tie: equally close to the reference mean |Δ| Naksha 0.01% · SimSolid 0.05%

Reference: {"citation": "NAFEMS, The Standard NAFEMS Benchmarks, Test No. T3. Glasgow: NAFEMS, Rev. 3, 1990.", "standard": "Abaqus Benchmarks Guide 4.3.3:…

QuantityReferenceNakshaΔSimSolid
Temperature at point C [C]36.636.60.0%−0.1%
VT09Thermal0.0%worst result
VT09SS-V 30800.0%

Heat Conduction with Temperature-dependent Conductivity

Naksha closer to the reference mean |Δ| Naksha 0.00% · SimSolid 0.87%

Reference: Kreith, F. Principles of Heat Transfer. 2nd ed. P.A.: International Textbook Co., 1959, pg.25

QuantityReferenceNakshaΔSimSolid
Thermal flux [BTU/(hr*ft^2)]29.7629.760.0%+0.9%
VTL01Thermo-structural · thermal-loading0.0%worst result
VTL01SS-V 40000.0%

Thermally Loaded Support Structure

Tie: equally close to the reference mean |Δ| Naksha 0.01% · SimSolid 0.05%

Reference: S. Timoshenko, Strength of Material, Part 1, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 30,…

QuantityReferenceNakshaΔSimSolid
Stress, Steel [psi]1.97e+041.97e+040.0%−0.1%
Stress, Copper [psi]1.015e+041.015e+040.0%0.0%
VTL02Thermo-structural · thermal-loading−0.8%worst result
VTL02SS-V 4010−0.8%

Bimetallic Cantilever Beam

Tie: equally close to the reference mean |Δ| Naksha 0.35% · SimSolid 0.28%

Reference: R.J. Roark, W.C. Young, Formulas for Stress and Strain, 5th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1975, pp. 113-114.

QuantityReferenceNakshaΔSimSolid
Free End, Middle Fiber, Disp X [in]0.0150.01496−0.2%+0.1%
Free End, Middle Fiber, Disp Y [in]0.750.750.0%+0.1%
Top Fiber, Stress [psi]75007438−0.8%−0.6%
VTL03Thermo-structural · thermal-loading0.0%worst result
VTL03SS-V 40200.0%

Coupled Thermal-Structural Analysis - Constrained Straight Bar Under Uniform Temperature

Naksha closer to the reference mean |Δ| Naksha 0.00% · SimSolid 0.16%

Reference: W.C. Young, R.G. Budynas, Roark’s Formulas for Stress and Strain, Seventh Edition, McGraw-Hill Book Co., Inc., 2001, p. 759.

QuantityReferenceNakshaΔSimSolid
Stress along bar (compression) [pa]2.52×1082.52×1080.0%−0.2%
VTL04Thermo-structural · thermal-loading0.0%worst result
VTL04SS-V 40300.0%

Coupled Thermal-Structural Analysis - Constrained Straight Bar Under Linear Temperature Field

Naksha closer to the reference mean |Δ| Naksha 0.00% · SimSolid 0.20%

Reference: W.C. Young, R.G. Budynas, Roark’s Formulas for Stress and Strain, Seventh Edition, McGraw-Hill Book Co., Inc., 2001, p. 759.

QuantityReferenceNakshaΔSimSolid
Stress at the top/bottom of the bar (compression/tension) [pa]2.52×1082.52×1080.0%−0.2%
Stress at the top/bottom of the bar (compression/tension) [pa]2.52×1082.52×1080.0%−0.2%
VNL01Nonlinear0.0%worst result
VNL01SS-V 50000.0%

Coupled Analysis - Bimetallic Beam Under Thermal Load

Naksha closer to the reference mean |Δ| Naksha 0.00% · SimSolid 0.56%

Reference: B.A. Boley, J.H. Weiner, Theory of Thermal Stress, R.E. Krieger Publishing Co, Malabar, FL, 1985, pg. (page number is blank on the page). '* Ref…

QuantityReferenceNakshaΔSimSolid
Temperature at Contact [def-F] [F]4004000.0%0.0%
Max Deflection [in] [in]0.90.90.0%−1.1%
VNL02Nonlinear · static, large deflection−2.5%worst result
VNL02SS-V 5010−2.5%

Z-Shaped Cantilever

Naksha closer to the reference mean |Δ| Naksha 1.18% · SimSolid 1.40%

Reference: A.A. Becker, Background to Finite Element Analysis of Geometric Non-linearity Benchmarks, Published by NAFEMS, Ref:-R0065, pg. 61 Page 66…

QuantityReferenceNakshaΔSimSolid
Uz at load 300 N [mm]113112−0.9%+0.3%
Uz at load 500 N [mm]124.1121−2.5%−1.6%
Uz at load 1000 N [mm]131129.6−1.0%+1.8%
Uz at load 2500 N [mm]139.5138.7−0.6%+2.8%
Uz at load 4000 N [mm]144142.6−1.0%+0.6%
VNL04Nonlinear+2.4%worst result
VNL04SS-V 5030+2.4%

Reactions at the Ends of Axially Loaded Plastic Bar

Tie: equally close to the reference mean |Δ| Naksha 1.12% · SimSolid 1.13%

Reference: No literature citation. One-dimensional analytical reference solution on the page: compatibility integral_0^A eps1 dx - integral_0^(L-A) eps2 dx =…

QuantityReferenceNakshaΔSimSolid
Reaction at F = 30000 N [N]1.713e+041.754e+04+2.4%+2.4%
Reaction at F = 47000 N [N]2.683e+042.695e+04+0.4%+0.6%
Reaction at F = 55000 N [N]3.14e+043.166e+04+0.8%+0.9%
Reaction at F = 60000 N [N]3.426e+043.454e+04+0.8%+0.7%
VNL05Nonlinear+5.7%worst result
VNL05SS-V 5040+5.7%

Residual Deformations in an Axially Loaded Plastic Bar

Naksha closer to the reference mean |Δ| Naksha 2.94% · SimSolid 3.05%

Reference: No literature citation. One-dimensional analytical reference: eps_r = eps - eps_e = (sigma/K)^(1/n) - sigma/E = (F/(K*A))^(1/n) - F/(E*A);…

QuantityReferenceNakshaΔSimSolid
Residual displacement at F = 20000 N [mm]3.223.302+2.5%+2.5%
Residual displacement at F = 25000 N [mm]9.169.217+0.6%+0.8%
Residual displacement at F = 30000 N [mm]19.0820.16+5.7%+5.9%
VNL07Nonlinear · static, separating contact−0.9%worst result
VNL07SS-V 5060−0.9%

Separate Beams

No SimSolid value to compare

Reference: No literature citation; analytical rigid-body equilibrium on the page.

QuantityReferenceNakshaΔSimSolid
Case 1 (Fx 0, Fy 1 N): Fy at which the beam tips about A [N]10.9906−0.9%—
Case 2 (Fx 0, Fy 0.9 N): contact force N = P - Fy [N]1.11.10.0%—
Case 2 (Fx 0, Fy 0.9 N): where N acts, from edge A [mm]9.0919.0940.0%—
Case 3 (Fx 0.3, Fy 0 N): friction force carried [N]0.30.30.0%—
Case 4 (Fx 0.31, Fy 0 N): end load at which the beam slides [N]0.30.2993−0.2%—
Case 5 (Fx 0.29, Fy 0 N): friction force carried [N]0.290.290.0%—
VNL08Nonlinear · static, large deflection+1.2%worst result
VNL08SS-V 5070+1.2%

Pinched Hemispherical Shell

Naksha closer to the reference mean |Δ| Naksha 0.83% · SimSolid 4.83%

Reference: Test 3DNLG-9 from NAFEMS Publication R0024 "A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3-D Beams and Shells (SUMMARY)."…

QuantityReferenceNakshaΔSimSolid
Table 1: Ux at Point A, P = 40 lbf [in]-3.28-3.304+0.7%−4.1%
Table 1: Ux at Point A, P = 60 lbf [in]-4.36-4.399+0.9%−5.5%
Table 1: Ux at Point A, P = 100 lbf [in]-5.95-5.989+0.7%−7.9%
Table 2: Uy at Point B, P = 40 lbf [in]-2.33-2.358+1.2%−2.7%
Table 2: Uy at Point B, P = 60 lbf [in]-2.83-2.858+1.0%−3.7%
Table 2: Uy at Point B, P = 100 lbf [in]-3.43-3.447+0.5%−5.1%
VNL09Nonlinear+6.5%worst result
VNL09SS-V 5080+6.5%

Rigid Punch Plasticity

SimSolid closer to the reference mean |Δ| Naksha 3.53% · SimSolid 3.15%

Reference: Test PL-7 from NAFEMS Publication R0049, "Background to Material Non-Linear Benchmarks".

QuantityReferenceNakshaΔSimSolid
Reaction, perfect plasticity, D = 0.04 mm [N per mm]3030.51+1.7%−1.0%
Reaction, perfect plasticity, D = 0.12 mm [N per mm]8690.6+5.4%+6.1%
Reaction, perfect plasticity, D = 0.14 mm [N per mm]99104.5+5.5%+5.1%
Reaction, perfect plasticity, D = 0.16 mm [N per mm]109111.7+2.5%−2.6%
Reaction, perfect plasticity, D = 0.18 mm [N per mm]110114.3+3.9%−2.5%
Reaction, perfect plasticity, D = 0.24 mm [N per mm]111118.2+6.5%−1.1%
Reaction, hardening, D = 0.04 mm [N per mm]3030.51+1.7%−1.1%
Reaction, hardening, D = 0.12 mm [N per mm]8790.74+4.3%+6.7%
Reaction, hardening, D = 0.14 mm [N per mm]100104.8+4.8%+8.2%
Reaction, hardening, D = 0.16 mm [N per mm]113113.4+0.3%−0.4%
Reaction, hardening, D = 0.18 mm [N per mm]114117.9+3.4%+2.3%
Reaction, hardening, D = 0.24 mm [N per mm]125128+2.4%+0.9%
VNL10Nonlinear0.0%worst result
VNL10SS-V 50900.0%

Bushing Stiffness

Tie: equally close to the reference mean |Δ| Naksha 0.00% · SimSolid 0.00%

Reference: *The reference is calculated by hand using a rotation of 1 radian about the cylinder axis (theta = M/k_rot = 10 N-m / 10 N-m/rad = 1 rad).

QuantityReferenceNakshaΔSimSolid
Rotation of Cylinder (rad) [rad]110.0%0.0%
VD01Dynamics · transient−8.7%worst result
VD01SS-V 6000−8.7%

Simply Supported Thin Square Plate - Harmonic Forced Vibration Response

Naksha closer to the reference mean |Δ| Naksha 4.40% · SimSolid 4.68%

Reference: Test 13H from NAFEMS Publication R0016, "Selected Benchmarks for Forced Vibration" J. Maguire, D.J. Dawswell, L. Gould

QuantityReferenceNakshaΔSimSolid
Deflection Y (peak) [mm]45.4245.36−0.1%−0.2%
Surface Stress (peak) [MPa]35.0832.04−8.7%−9.2%
VD02Dynamics · transient+2.8%worst result
VD02SS-V 6010+2.8%

Simply Supported Thin Square Plate - Periodic Forced Vibration Response

SimSolid closer to the reference mean |Δ| Naksha 1.84% · SimSolid 1.49%

Reference: Test 13P from NAFEMS Publication R0016, "Selected Benchmarks for Forced Vibration" J. Maguire, D.J. Dawswell, L. Gould

QuantityReferenceNakshaΔSimSolid
Deflection Y (steady-state) [mm]-2.863-2.889+0.9%+0.8%
Surface Stress (steady-state) [MPa]2.0182.074+2.8%+2.2%
VD03Dynamics · transient−2.4%worst result
VD03SS-V 6020−2.4%

Simply Supported Thin Square Plate - Transient Forced Vibration Response

Naksha closer to the reference mean |Δ| Naksha 1.60% · SimSolid 2.71%

Reference: Test 13T from NAFEMS Publication R0016, "Selected Benchmarks for Forced Vibration" J. Maguire, D.J. Dawswell, L. Gould

QuantityReferenceNakshaΔSimSolid
Peak Time [sec]0.210.211+0.5%0.0%
Deflection Y (peak) [mm]-3.52-3.454−1.9%−1.7%
Surface Stress (peak) [MPa]2.412.351−2.4%−6.4%
VD04Dynamics · harmonic−8.4%worst result
VD04SS-V 6030−8.4%

Simply Supported Thin Square Plate - Frequency Response

Naksha closer to the reference mean |Δ| Naksha 4.28% · SimSolid 4.56%

Reference: Test 13H from NAFEMS Publication R0016, "Selected Benchmarks for Forced Vibration" J. Maguire, D.J. Dawswell, L. Gould

QuantityReferenceNakshaΔSimSolid
Deflection Y Amplitude (peak) [mm]45.4245.49+0.1%+0.6%
Surface Stress Amplitude (peak) [MPa]35.0832.13−8.4%−8.6%
VD05Dynamics · random+0.7%worst result
VD05SS-V 6040+0.7%

Simply Supported Thin Square Plate - Random Forced Vibration Response

Naksha closer to the reference mean |Δ| Naksha 0.47% · SimSolid 0.77%

Reference: Test 13H from NAFEMS Publication R0016, "Selected Benchmarks for Forced Vibration" J. Maguire, D.J. Dawswell, L. Gould (as printed; the random…

QuantityReferenceNakshaΔSimSolid
PSD Y-displacement (peak) [mm2/Hz]20632069+0.3%+1.1%
PSD Surface Stress X (peak) [MPa2/Hz]10251032+0.7%+0.4%
VC01Composites+1.7%worst result
VC01SS-V 8000+1.7%

Laminated Strip

Naksha closer to the reference mean |Δ| Naksha 0.75% · SimSolid 0.94%

Reference: NAFEMS R0031 - Composite Benchmarks, Hardy 2001

QuantityReferenceNakshaΔSimSolid
Z deflection at E [mm]-1.06-1.058−0.2%−0.1%
Bending Stress at E [MPa]683.9686.4+0.4%+1.9%
Interlaminar shear stress at D [MPa]-4.1-4.172+1.7%−0.8%
VC02Composites−2.9%worst result
VC02SS-V 8010−2.9%

Wrapped Thick Cylinder under Pressure and Thermal Loading

SimSolid closer to the reference mean |Δ| Naksha 1.29% · SimSolid 1.13%

Reference: {"citation": "Test R0031/2 from NAFEMS publication R0031, Composites Benchmarks, February 1995", "standard_reference_values": {"source": "Abaqus…

QuantityReferenceNakshaΔSimSolid
Hoop Stress, Case 1, at radius = 24 mm [MPa]14831484+0.1%−1.4%
Hoop Stress, Case 1, at radius = 26 mm [MPa]822797.8−2.9%−0.9%
Hoop Stress, Case 2, at radius = 24 mm [MPa]130913080.0%−1.8%
Hoop Stress, Case 2, at radius = 26 mm [MPa]994973.3−2.1%+0.4%
VE05Electromagnetic · electromagnetic modes (lossy)+0.8%worst result
VE05SS-V 9004+0.8%

Resonator with Conducting Material

No SimSolid value to compare

Reference: 1 Jianming, J., The finite element method in electromagnetics, 3rd Edition, John Wiley & Sons, Inc., 2014, Ex.12.8. 2 Pozar, D.M., Microwave…

QuantityReferenceNakshaΔSimSolid
TE101 overdamped root 1: decay rate [1/s]3.6×10103.6×1010−0.1%—
TE101 overdamped root 2: decay rate [1/s]7.69×10107.69×10100.0%—
Mode at 5.6186 GHz (x1): frequency [GHz]5.6195.663+0.8%—
Mode at 10.0888 GHz (x1): frequency [GHz]10.0910.1+0.1%—
Mode at 12.5680 GHz (x2): frequency [GHz]12.5712.570.0%—
Mode at 14.1451 GHz (x4): frequency [GHz]14.1514.140.0%—
Mode at 14.6331 GHz (x2): frequency [GHz]14.6314.7+0.4%—
Mode at 16.0080 GHz (x2): frequency [GHz]16.0116.010.0%—
Mode at 16.4408 GHz (x2): frequency [GHz]16.4416.42−0.1%—
Decay rate of every oscillating mode [1/s]5.65×10105.65×10100.0%—

How to read the gallery

  • Δ is (Naksha ÷ reference − 1). The badge on each card is its worst result. Green is within 2%, amber 2–5%, red over 5%.
  • The reference is the theory, handbook or standard benchmark value cited for each problem. The SimSolid column is the deviation of SimSolid's own result, as published in its verification manual, from the same reference.
  • In each row, the result closer to the reference is highlighted. The verdict on each card compares the mean |Δ| over all the problem's results; under 0.1 percentage points apart counts as a tie.
  • Only problems whose geometry is fully stated by dimensions are shown. We left out problems whose shape or key positions had to be measured from a picture, plus a few whose dimensions or reference values are only given as charts.

What we left out, and why

14 problems from the manual are not in the gallery. We applied one rule to both tools: a problem is shown only if its geometry and reference values are fully stated. For transparency, here is every exclusion, with Naksha's own worst result where we ran it.

CaseProblemWhy it's excludedNaksha worst result
VS12Notched PlateNotch position measured from figure pixels17.6%
VM07In-plane Vibration of Pin-ended CrossArm lengths read off the figure; pin position not dimensioned5.8%
VS18Stress Concentration of a Plate with Eccentric HoleHole position relation read from a chart14.9%
VNL03Lateral Buckling of a Right Angle FrameReference values digitised from plotted curves58.0%
VS10Stepped Shaft with FilletShaft segment lengths not stated22.7%
VS15Stress Concentration of Filleted BarSegment lengths, supports and load not stated15.0%
VS17Stress Concentration in a Groove ShaftShaft length and groove position not stated7.9%
VS19Stress Concentration in a Filleted NotchSegment lengths and support not stated26.2%
VS20Stress Concentration of a Plate with Semi-circular HolesNotch spacing, count and plate length not statednot run
VF01SN Uniaxial FatigueNo dimensions given (shape only)not run
VE01Wave Propagation in a WaveguideKey dimensions given only in figuresnot run
VE02Wave Reflection on Dielectric BoundarySection arrangement given only in figuresnot run
VE03Wave Propagation in Loaded WaveguideNo numeric results; section placement figure-onlynot run
VE04Resonator with Two MaterialsNo numeric results; slab position figure-onlynot run

Corrections

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Problem definitions and SimSolid results are taken from the publicly available SimSolid Verification Manual on help.altair.com, and are used to identify the problems and to compare published results. Altair®, SimSolid® and OpenRadioss™ are trademarks of Altair Engineering, Inc., now part of Siemens. Naksha and Effileap aren't affiliated with or endorsed by Altair or Siemens. See Terms & trademarks.

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