NAFEMS R0031/1: Fixed-End Beam Natural Frequencies

The NAFEMS R0031 benchmark. Natural frequencies of a fixed-fixed beam. Verifies agreement with the reference value for the first mode.

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrices and construct the global stiffness equation.

We transform it into the weak form (variational form) and use the Galerkin method formulation with test functions and shape functions. The choice of element type (low-order elements vs. higher-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

We solve the system of equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Developed in the 1960s as NASA Structural Analysis (NASTRAN). Commercialized by MSC Software, later UGS (now Siemens) derived NX Nastran. MSC was acquired by Hexagon AB in 2017.

Current Affiliation: MSC Nastran (Hexagon), NX Nastran (Siemens Digital Industries Software)

Developed in 1978 by HKS (Hibbitt, Karlsson & Sorensen). Acquired by Dassault Systèmes in 2005 and integrated into the SIMULIA brand.

Current Affiliation: Dassault Systèmes SIMULIA

Developed in 1970 by Swanson Analysis Systems Inc. (SASI). Based on APDL (Ansys Parametric Design Language).

Current Affiliation: Ansys Inc.

When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, higher-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.