Inverse differential quadrature based shell strong unified formulation for 3D stress analysis of composite shell structures

Shell structures stand as one of the most efficient and widely adopted structural elements across mechanical, civil, and aerospace engineering, offering efficient load transfer through coupled in-plane and bending actions. When combined with fibre-reinforced polymer composites, their structural performance is enhanced by enabling tailored mechanical responses through material lay-up configurations. Due to the strong dependence of composite shell behaviour on the shell thickness-to-radius of curvature ratio, high-fidelity, tunable higher-order theories are essential to capture complex structural responses accurately. Simultaneously, robust numerical methods are needed to evaluate derivatives of the field variables precisely for enhanced stress, strain, and displacement predictions. To address these challenges, this study introduces a novel strong-form framework: SSUF-iDQM, by integrating variable order kinematics-based Shell Strong Unified Formulation (SSUF) with the Inverse Differential Quadrature Method (iDQM) that circumvents differentiation-induced errors in higher-order systems. The framework is further enhanced with a robust yet simple 3D stress-recovery scheme to reconstruct through-thickness interlaminar transverse stresses, capturing complex through-thickness behaviour like stress reversals in bending-dominated shells. Demonstrating its broad applicability, SSUF-iDQM is applied across spherical, cylindrical, and flat composite and sandwich structures. It exhibits excellent accuracy within error margins of 0.5% for spherical shells and 0.3% for cylindrical shells while using only 0.37% of the degrees of freedom of 3D finite element models. In soft-core sandwich shells, the stress-recovery yields errors as low as 0.01%, confirming its effectiveness. Free from thin-shell assumptions ( (Formula presented) ), SSUF-iDQM remains effective for thin to thick shells and is adaptable for a wide range of mechanical theories and complex structural problems.