Finite Element Analysis of Shell Structures

Finite element analysis (FEA) of shell structures encompasses the numerical simulation of thin‐walled, curved bodies subject to mechanical loads and environmental effects. Shell elements combine membrane and bending behaviour to capture the response of aerospace skins, architectural canopies, automotive panels and marine hulls with high fidelity. Classical theories, notably the Kirchhoff–Love formulation for thin shells and the Reissner–Mindlin approach for moderately thick shells, underpin most modern implementations. Key challenges include geometric nonlinearity, where large deformations alter the stiffness and load path; numerical locking, which artificially stiffens the solution in bending‐dominated problems; and mesh distortion sensitivity, which can degrade accuracy in complex geometries. Recent methodological advances address these issues through enhanced variational formulations, mixed interpolation schemes, reduced or selective integration techniques and stabilisation strategies. Concurrent developments in computational hardware and solver algorithms have enabled transient dynamic and modal analyses for stability and vibration studies. As global demands for lightweight, resilient and energy-efficient structures grow, FEA of shells remains central to multidisciplinary design optimisation, performance prediction under extreme conditions and the integration of novel materials such as composites and functionally graded laminates.

Research from Nature Portfolio

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Research from all publishers

Recent work has introduced a nonlinear flat shell element tailored for highly flexible wind turbine blades with continuously varying thickness. A co-rotational formulation captures large geometric rotations and updates the stiffness matrix via an interpolated thickness function. Validation against static and modal tests shows close agreement with reference solid models and commercial software, demonstrating accuracy in both static load and dynamic vibration analyses.

A novel penalty partial reduced selective integration method has been proposed to eliminate membrane and shear locking in thin steel and concrete shells. By splitting the shear energy into fully and selectively integrated components with calibrated weight coefficients, the formulation delivers robust accuracy across a broad set of analytical and experimental benchmarks. Comparative studies reveal superior predictive capability relative to established shell elements, with straightforward guidelines for selecting integration parameters.

An extensive examination of benchmark problems for shell finite element models emphasises the importance of provenance, completeness and suitability of test cases. The study identifies a core set of limit‐value and deformation scenarios that effectively verify patch tests, mesh distortion resilience and nonlinear response. This framework promotes consistency in element development and facilitates cross-comparison among diverse formulations.

Finite Element Analysis of Shell Structures publication trend

The graph below shows the total number of articles in finite element analysis of shell structures across all publications each year (not limited to Nature Index journals).

Technical terms

Finite element analysis (FEA): Numerical technique for approximating solutions to boundary-value problems by subdividing structures into discrete elements.

Shell element: A specialised finite element that represents thin, curved structures by combining in-plane membrane and out-of-plane bending behaviour.

Locking: Numerical artefact causing excessive stiffness in bending or shear, often affecting low-order elements in thin-shell analyses.

Co-rotational method: Technique that isolates rigid-body rotations and applies linear stiffness updates in a rotating local frame to handle large deformations.

Reduced selective integration: Integration strategy that lowers the order of numerical quadrature for certain strain components to alleviate locking phenomena.

Stiffness matrix: Mathematical representation of an element’s resistance to deformation, relating nodal displacements to applied forces.

References

1. Development of nonlinear flat shell element with nonlinear thickness variation for highly flexible wind turbine blade. Renewable Energy (2024).
2. Penalty partial reduced selective integration: a new method to solve locking phenomena in thin shell steel and concrete structures. Curved and Layered Structures (2022).
3. Benchmarking Computational Shell Models. Archives of Computational Methods in Engineering (2022).