Hybrid quasi-Trefftz 3-D finite elements for laminated composite plates

Three-dimensional hybrid finite elements are proposed to the analysis of laminated composite plates. Two independent fields are approximated: stresses within the elements and displacements on their boundary. The required stress field in point-wise equilibrium is generated by harmonic and orthogonal hierarchical polynomials, adapted from Papkovitch–Neuber solution of Navier equations for isotropic material. The solving system is symmetric, highly sparse and well conditioned. The elements are suited to p-refinement and present low sensitivity to mesh distortion. Illustrative applications are given to evaluate displacements and stresses.

► A new hybrid stress formulation of finite element has been proposed.
► Stress field in point-wise equilibrium is generated by harmonic and orthogonal polynomials.
► Many DOF are involved, but substantial memory and computing time are saved.
► Illustrative applications are given to evaluate displacements and stresses.
► Good estimation for displacements and stresses is achieved.