Abstract The virtual element method (VEM) was developed not too long ago, starting with the paper [2] related to elasticity in solid mechanics. allows revisit construction of different elements; however, it has so far applied one-dimensional structures like trusses and beams. Here we study several VEM elements suitable for beams show that methodology produces are equivalent well-known finite bu...

This paper contains two main parts. First, applications of Trefftz finite element methods to mode III fracture problems are presented in this paper. Trial functions for electoelastic fields are presented for both regular element and cracked element. These functions are used in deriving Trefftz finite element formulation together with modified variational principle. The performance of the propos...