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

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.