T-spline based isogeometric solid element with locally varying mesh in nonlinear dynamics

Abstract

To solve nonlinear dynamic problems in three-dimensional space, this investigation presents a new isogeometric solid element and nonlinear strain field of the proposed element through coordinate transformation in tensor analysis. In order to make the proposed element can be used seamlessly in computer aided design (CAD) and computer aided engineering (CAE) systems, trivariate T-spline is adopted as the basis function of the isogeometric solid element. Local mesh update algorithms are developed for T-spline based isogeometric solid element in virtue of Bézier projection method. Mesh is refined locally in important regions to obtain accurate results and redundant elements are coarsened beyond important regions to improve computational efficiency. Therefore, the computational efficiency and the computational accuracy are balanced in nonlinear dynamics analysis. Three statics numerical examples are set to test the correctness of the elemental elastic model. A flexible pendulum simulation is performed to study the dynamics characteristic of the proposed element. An experiment is implemented to test the proposed element’s ability to solve nonlinear dynamics problems. A simulation that a flexible pendulum contacts with a stick is performed and local mesh update algorithms are employed. The computation results and computation time are analyzed to research the effectiveness of the proposed locally varying mesh T-spline based solid element in nonlinear dynamics problems.