Inverse differential quadrature solutions for free vibration of arbitrary shaped laminated plate structures

An essential aspect of design of laminated plate structures in many engineering applications is the analysis of free vibration behaviour in order to model the structure for random excitations. In this regard, numerical solutions to the systems of high-order partial differential equations governing free vibration response of the structure become important. Direct approximation of such high-order systems are prone to error arising from the sensitivity of high-order numerical differentiation to noise necessitating the demand for improved solution techniques. In this work, a novel generalised inverse differential quadrature method is developed to study the dynamic behaviour of first-order shear deformable arbitrary-shaped laminated plates. The ensuing underdetermined system is operated upon by Moore–Penrose pseudo-inverse preconditioning to form a squared eigenvalue system. Free vibration solutions of square, skew, circular, and annular sector plates for different boundary conditions are obtained and validated against exact and numerical solutions in the literature and ABAQUS. It is demonstrated with numerous examples that iDQM solutions are in excellent agreement with exact solutions for square plates and the results for arbitrary shaped plates are comparable with solutions in the literature while saving up to 96% degrees of freedom required for ABAQUS solution. Finally, refined parametric studies conducted reveal that, subject to varying geometric configurations, iDQM solutions are numerically stable and potentially converge faster than DQM </p

Efficient three-dimensional geometrically nonlinear analysis of variable stiffness composite beams using strong unified formulation

The use of composite laminates for advanced structural applications has increased recently, due in part to their ability for tailoring material properties to meet specific requirements. In this regard, variable stiffness (VS) designs have potential for improved performance over constant stiffness designs, made possible by fibre placement technologies which permit steering of the fibre path to achieve variable in-plane orientation. However, due to the expanded, large design space, computationally expensive routines are required to fully explore the potential of VS designs. This computational requirement is further complicated when VS composites are deployed for applications involving nonlinear large deflections which often necessitate complex 3D stress predictions to accurately account for localised stresses. In this work, we develop a geometrically nonlinear strong Unified Formulation (SUF) for the 3D stress analysis of VS composite structures undergoing large deflections. A single domain differential quadrature method-based 1D element coupled with a serendipity Lagrange-based 2D finite element are used to capture the kinematics of the 3D structure in the axial and cross sectional dimensions, respectively. Predictions from SUF compare favourably against those in the literature as well as with those from ABAQUS 3D finite element models, yet also show significant enhanced computational efficiency. Results from the nonlinear large deflection analysis demonstrate the potential of variable stiffness properties to achieve enhanced structural response of composite laminates due to the variation of coupling effects in different loading regimes