Meshfree Method for Geometrical Nonlinear Analysis of Curved and Twisted Beams Using a Three-Dimensional Finite Deformation Theory

Abstract

This paper presents a three-dimensional finite deformation theory for the geometric nonlinear analysis of both the curved and twisted beams using the meshfree method based on the Timoshenko beam hypothesis. The theory presented is simple, but it is capable of solving the stability, postbuckling, snap-through, and large deformation problems effectively. Clear physical meanings will be revealed in derivation of the three-dimensional finite deformation theory. A meshfree method based on the differential reproducing kernel (DRK) approximation collocation method combined with the Newton–Raphson method is employed to solve the strong forms of the geometrically nonlinear problems. Numerical examples are given to illustrate the validity of the method presented.

Inclined Curved Crack Composite Beam: Experimental and Computational Analysis with Recycled Aluminum Composite Materials and Comparison with an Artificial Neural Network

“…The mechanical structure is most important in practical engineering applications. Due to the limitations of the analytical method, especially in solving a curved crack beam, a variety of numerical methods have been developed using the finite element method, transfer matrix method, differential quadrature method, meshfree , isogeometric analysis, , meshless method, , and, recently, deep learning-based methods. − …”