Line Elements for the Multiphysics Modeling of Axispherical Bodies

摘要

A simple novel line element is presented for the multiphysics modeling of spherically symmetric geometries. The element is highly computationally efficient when compared with its solid and axicylindrical cousins. Both displacement based and assumed stress formulations are considered. Structural applications considered include elastostatics, piezoelectricity and plasticity. A formulation for the accommodation of radially asymmetric loading is also suggested. Envisaged applications of the elements include spherical micro-electro-mechanical systems (MEMS). Spherical MEMS devices are perceived to be important in a number of applications. They are unidirectional, an attractive feature when the to-be-sensed quantity is of unknown location in an effectively infinite field. Spherical devices are, for example, used on a very large scale in active and passive sonar arrays. While many an axispherical problem can of course be solved analytically, this becomes very difficult, and even infeasible, when multiphysics phenomena and, for example, plasticity effects are considered. The accommodation of asymmetric loads via spherical harmonics further increase the applicability of the one-dimensional elements.