Weak-form differential quadrature element analysis of plate on a tensionless and frictional foundation using a higher-order kinematics

摘要

Plate-foundation systems, as a structure common in engineering practices, have received extensive scientific research. A novel technical scheme is proposed to improve the com-putational efficiency in predicting the nonlinear responses of a plate on the foundation. The core work of this technical scheme lies in two aspects. The first aspect is to create a novel plate-foundation system, where a higher order kinematical assumption common in Carrera Unified Formulation is used to model the plate, and a plate-foundation interac-tion model taking into account the tensionless and frictional characteristics is created. The adjustable kinematical parameters of the higher-order kinematical assumption endow the plate with flexible accuracy. The second aspect is to derive a two-dimensional (2D) dif-ferential quadrature (DQ) formula for 2D interpolation based on the one-dimensional (1D) DQ formula, and thus a weak-form differential quadrature element method (WDQEM) for nonlinear quasi-static analysis of the plate-foundation system is proposed by using the principle of virtual work and the 2D interpolation derived. The proposed WDQEM sup-ports flexible nodal configuration in the element, making it degree-of-freedom-flexible and suitable to carry out both p -and h-version strategies in the numerical simulation. Several numerical examples are given to (i) verify the proposed technical scheme and the corre-sponding computer codes; (ii) to investigate the numerical performance of the WDQEM through comparison between the classical plate model and the 3D solid model, and (iii) to study some physical behaviors related to the tensionless and frictional characteristics of the plate-foundation system. The example results show that (i) the WDQEM converges much faster than the conventional finite element method due to the higher order approx-imation; (ii) the higher order kinematics, due to its capability of adjusting the accuracy of kinematical assumptions, can effectively reduce the computational scale; (iii) the smooth-ness problem in the post process of stresses analysis is greatly alleviated, (iv) the ten-sionless and frictional features of the plate-foundation system should be considered when evaluating both the vertical and horizontal bearing capacities of the plate.

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