Efficient strong Unified Formulation for stress analysis of non-prismatic beam structures

The Unified Formulation (UF) has gained attention as a powerful tool for efficient design of structural components. Due to the inherent flexibility of its kinematics representation, arbitrary shape functions can be selected in different dimensions to achieve a high-fidelity characterisation of structural response under load. Despite this merit, the classical isoparametric description of UF limits the application to prismatic structures. The weak-form anisoparametric approach adopted to overcome this limitation in a recent work by Patni et al. proves to be versatile yet computationally challenging owing to the expensive computation of its UF stiffness matrix by means of full volume integrals. We propose a strong-form anisoparametric UF (SUF) based on the Serendipity Lagrange Expansion (SLE) cross-sectional finite element and differential quadrature beam element. The main objective of the SUF is to achieve an efficient computation of the UF stiffness matrix by restricting Gauss operations to the variable cross-sections of non-prismatic structures in a discrete sense, thus eliminating the need for full volume integrals. When assessed against weak-form based UF, ABAQUS FE and analytical solutions, the static analysis of non-prismatic beam-like structures under different loads by the SUF is shown to be accurate, numerically stable, and computationally more efficient than state-of-the-art methods.