Finite Element Modeling Techniques in Structural Analysis

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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Recent developments have targeted the dual challenges of mesh distortion and numerical locking. A novel Petrov–Galerkin low-order enhanced assumed strain element demonstrates locking-free behaviour and mesh-distortion insensitivity by enforcing exact patch-test conditions and augmented strain fields, yielding accurate bending and coarse-mesh predictions. Advances in error estimation have been achieved through radial point interpolation-based recovery techniques, which combine radial basis functions with polynomial bases to reconstruct displacement and pressure fields; adaptive refinement guided by energy-norm error distributions notably enhances convergence for incompressible elasticity. Furthermore, an eight-node plane hybrid element grounded in the Hellinger–Reissner variational principle integrates fifteen stress-mode parameters chosen to eliminate spurious zero-energy modes, overcoming shear and volumetric locking across varying cross sections while preserving computational efficiency. These contributions exemplify a shift towards versatile formulations that maintain fidelity under severe mesh irregularities and complex material behaviours.

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

1. Mesh distortion insensitive and locking‐free Petrov–Galerkin low‐order EAS elements for linear elasticity. International Journal for Numerical Methods in Engineering (2021).
2. Radial Point Interpolation-Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems. Applied Sciences (2023).
3. An 8-Node Plane Hybrid Element for Structural Mechanics Problems Based on the Hellinger-Reissner Variational Principle. Computer Modeling in Engineering & Sciences (2024).
4. Hellinger–Reissner variational principle for a class of specified stress problems. International Journal of Nonlinear Sciences and Numerical Simulation (2022).