journal article·2025-03-11Open access

Comparative Analysis of In-Plane and Out-of-Plane Bending Benchmarks Using Two Finite Element Packages

Emilia Słota, Adam Wosatko

Applied Sciences· Volume 15· Issue 6

Abstract

An essential aspect of design from the perspective of structural strength is the reliability of the results obtained during the computations for the analyzed model. Among various skills in numerical analysis, an engineer should be able to independently verify the quality of the available software using benchmarks already at the level of statics. An effective method of such verification is comparing the test results obtained from two different packages. The paper discusses three structure-oriented benchmarks for in-plane and out-of-plane bending of a flat membrane and a slab, respectively. The computations are carried out using the Robot and Midas finite element tools. These simulation tests are selected to present issues related to the modeling of bending, which is crucial for reliable design: the convergence of the solution for a cantilever, the possibility of a reduction in slab moments above columns, and the interaction effects between the beam and the plate, depending on their position and connection in the model. It is shown that, in finite element calculations, attention must be paid to avoiding errors due to improper data input and software option settings, leading to incorrect simulation results, which may negatively impact the design process. A proper understanding of software tools, for example, through benchmark verification, ensures their conscious use in developing more complex structural models.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Laser and Thermal Forming Techniques · Metal Forming Simulation Techniques · Composite Structure Analysis and Optimization

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Faculty of Civil Engineering, Cracow University of Technology, Warszawska 24, 31-155 Cracow, Poland

Synergia Konstrukcje Budowlane, Fredry 2, 30-605 Cracow, Poland

Funding

Faculty of Civil Engineering at the Cracow University of Technology

References (43)

Show source-provided references
1. Defining conceptual artefacts to manage and design simplicities in complex adaptive systems10.1016/j.heliyon.2024.e41033 ↗
2. Complex computer simulations, numerical artifacts, and numerical phenomena10.15837/ijccc.2010.5.2234 ↗
3. Hitchings, D., Kamoulakos, A., Davies, G., and NAFEMS (2025, February 05). Linear Static Benchmarks—Volume 1. Available online: https://www.nafems.org/publications/browse_buy/browse_by_topic/linear/p07/.
4. Hitchings, D., and NAFEMS (2025, February 05). Linear Static Benchmarks—Volume 2. Available online: https://www.nafems.org/publications/browse_buy/browse_by_topic/linear/p08/.
5. A proposed standard set of problems to test finite element accuracy10.1016/0168-874X(85)90003-4 ↗
6. Shell finite elements with six degrees of freedom per node
7. A review and catalogue of plate bending finite elements10.1016/0045-7949(84)90055-5 ↗
9. (2025, February 05). Robot Structural Analysis. Available online: http://www.autodesk.com/products/robot-structural-analysis.
10. (2025, February 05). Midas nGEN. Available online: https://resource.midasuser.com/en/product/ngen/overview.
11. Reddy, J.N. (2006). Theory and Analysis of Elastic Plates and Shells, CRC Press/Taylor & Francis. [2nd ed.].10.1201/9780849384165 ↗
12. Radwańska, M., Stankiewicz, A., Wosatko, A., and Pamin, J. (2017). Plate and Shell Structures. Selected Analytical and Finite Element Solutions, John Wiley & Sons.10.1002/9781118934531 ↗
13. A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields—Part I: An extended DKT element for thick-plate bending analysis10.1002/nme.1620361106 ↗
14. A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields—Part II: An extended DKQ element for thick-plate bending analysis10.1002/nme.1620361107 ↗
15. Evaluation of the constant strain triangle with drilling rotations10.1002/nme.1620261205 ↗
16. A robust quadrilateral membrane finite element with drilling degrees of freedom10.1002/nme.1620300305 ↗
17. A study of optimal membrane triangles with drilling freedoms10.1016/S0045-7825(03)00253-6 ↗
18. Cook, R.D., Malkus, D.S., Plesha, M.E., and Witt, R.J. (2001). Concepts and Applications of Finite Element Analysis, John Wiley & Sons. [4th ed.].
19. Hartmann, F., and Katz, C. (2007). Structural Analysis with Finite Elements, Springer. [2nd ed.].10.1007/978-3-540-49702-8 ↗
20. Belytschko, T., Liu, W.K., Moran, B., and Elkhodary, K.I. (2014). Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons. [2nd ed.].
21. Geometrically nonlinear analysis of shells—Benchmark problems for Autocad Robot Analysis Professional
22. Ambroziak, A. (2023, January 28–31). Modelowanie numeryczne istnieja̧cych konstrukcji żelbetowych. Proceedings of the XXXVII Ogólnopolskie Warsztaty Pracy Projektanta Konstrukcji, Wisła, Poland. (In Polish).
23. Timoshenko, S., and Goodier, J.N. (1951). Theory of Elasticity, McGraw-Hill. [2nd ed.].
24. Girkmann, K. (1956). Flächentragwerke: Einführung in die Elastostatik der Scheiben, Platten, Schalen und Faltwerke, Springer. (In German).10.1007/978-3-7091-4386-5 ↗
25. Radzik, Ł. (2013, January 18–20). Projektowanie stropów płytowo-słupowych w kontekście komputerowego wspomagania projektowania. Proceedings of the II Konferencja Studentów i Doktorantów Wydziału Budownictwa Lądowego i Wodnego, Szklarska Poręba, Poland. (In Polish).
26. Finite element modeling assumptions impact on seismic response demands of MRF-buildings10.1007/s11803-018-0478-1 ↗
27. Who developed the so-called Timoshenko beam theory?10.1177/1081286519856931 ↗
28. Closed-form analytical solution to the problem of bending of a multilayer composite beam—Derivation and verification10.1016/j.compstruct.2022.115611 ↗
29. A triangular membrane element with rotational degrees of freedom10.1016/0045-7825(85)90113-6 ↗
30. A unified formulation for triangular and quadrilateral flat shell finite elements with six nodal degrees of freedom10.1002/cnm.1630070102 ↗
31. Elastoplastic law of Cosserat type in shell theory with drilling rotation10.1177/1081286514554351 ↗
32. Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z. (2013). The Finite Element Method: Its Basis and Fundamentals, Elsevier, Butterworth-Heinemann. [7th ed.].
33. Stress singularities in classical elasticity—I: Removal, interpretation, and analysis10.1115/1.1762503 ↗
34. Modeling of singular stress fields using finite element method10.1016/S0020-7683(02)00371-2 ↗
35. The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique10.1002/nme.1620330702 ↗
36. Adaptive FE analysis of RC shells. I: Theory10.1061/(ASCE)0733-9399(2001)127:12(1203) ↗
37. A study of localization limiters for strain-softening in statics and dynamics10.1016/0045-7949(89)90244-7 ↗
38. Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results10.1016/j.ijsolstr.2011.03.006 ↗
39. Simulations of thermal softening in large strain thermoplasticity
40. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations10.1002/nme.2861 ↗
41. Makvandi, R. (2021). Overcoming Stress Singularities: Combining Phase-Field Modelling of Fracture, Strain Gradient Theory, and Isogeometric Analysis. [Ph.D. Thesis, Otto von Guericke University].
42. Radzik, Ł. (2025, February 05). Autodesk Robot—Offsety (Belka Pod Płytą). (In Polish).
43. Starosolski, W. (2022). Komputerowe Modelowanie Betonowych Ustrojów Inżynierskich—Wybrane Zagadnienia, Politechnika Śląska. (In Polish).