Finite Element Modeling Techniques in Structural Analysis
Summary
The finite element method (FEM) has become the cornerstone of structural analysis, enabling the simulation of complex geometries and material behaviours under varied loading conditions. At its core, FEM discretises a continuum into interconnected elements, each governed by shape functions and constitutive relations. Recent advances have focused on overcoming classical limitations such as locking, mesh sensitivity and convergence difficulties in non-linear or near-incompressible regimes. Enhanced assumed strain (EAS) and hybrid stress–function approaches introduce additional internal parameters or stress modes to enrich element performance, while Petrov–Galerkin formulations tailor test functions to mitigate mesh distortion effects. Mixed variational principles, notably the Hellinger–Reissner framework, treat stress and displacement as independent variables, improving accuracy in specified stress problems. Concurrently, adaptive error estimation and mesh-refinement strategies—often employing radial basis or polynomial interpolation—yield automatic control of discretisation error. Collectively, these innovations underpin robust, efficient algorithms that meet the demands of aerospace, civil and mechanical engineering, where predictive fidelity and computational economy are paramount.
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Finite Element Modeling Techniques in Structural Analysis publication trend
The graph below shows the total number of articles in finite element modeling techniques in structural analysis across all publications each year (not limited to Nature Index journals).
Technical terms
Finite Element Method (FEM): A numerical approach that subdivides a structure into discrete elements to approximate physical responses.
Locking: A computational artefact causing artificial stiffness in elements, particularly in bending or near-incompressible analyses.
Mesh distortion: Deviation of element shapes from ideal configurations, often degrading solution accuracy.
Hellinger–Reissner principle: A mixed variational formulation treating stress and displacement as independent fields for enhanced accuracy.
Radial basis function (RBF): A smooth interpolation function centred at nodes, used to recover and refine finite element solutions.
References
- Mesh distortion insensitive and locking‐free Petrov–Galerkin low‐order EAS elements for linear elasticity. International Journal for Numerical Methods in Engineering (2021).
- Radial Point Interpolation-Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems. Applied Sciences (2023).
- An 8-Node Plane Hybrid Element for Structural Mechanics Problems Based on the Hellinger-Reissner Variational Principle. Computer Modeling in Engineering & Sciences (2024).
- Hellinger–Reissner variational principle for a class of specified stress problems. International Journal of Nonlinear Sciences and Numerical Simulation (2022).
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