State-of-the-Art in Different Formulations of Super Convergent Mesh-Less Differential Quadrature Method

Abstract

The primary objective of this study is to provide a literature review on the use of various kinds of differential quadrature techniques in the area of structural dynamics.The studies mostly focus on analyzing the buckling, free, and forced vibrations of isotropic and anisotropic beams and plates. The research study does not claim to be comprehensive; hence, certain choices must be made. The papers discussed in this article pertain to various formulations of differential quadrature methods, including the generalized method, inverse differential quadrature, differential quadrature element method, variational differential quadrature method, cubic-spline-based differential quadrature method, and radial basis function-based differential quadrature method. We assess the significant publications and challenges that have used these techniques. © The Author(s) under exclusive licence to International Center for Numerical Methods in Engineering (CIMNE) 2025.