A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model

Abstract

Building upon recent works devoted to the development of a stress-based layerwise model for multilayered plates, we explore an alternative finite-element discretization to the conventional displacement-based finite-element method. We rely on a mixed finite-element approach where both stresses and displacements are interpolated. Since conforming stress-based finite-elements ensuring traction continuity are difficult to construct, we consider a hybridization strategy in which traction continuity is relaxed by the introduction of an additional displacement-like Lagrange multiplier defined on the element facets. Such a strategy offers the advantage of uncoupling many degrees of freedom so that static condensation can be performed at the element level, yielding a much smaller final system to solve. Illustrative applications demonstrate that the proposed mixed approach is free from any shear-locking in the thin plate limit and is more accurate than a displacement approach for the same number of degrees of freedom. As a result, this method can be used to capture efficiently strong intra- and inter-laminar stress variations near free-edges or cracks.

Formulation for Multiple Cracks Problem in Thermoelectric-Bonded Materials Using Hypersingular Integral Equations

“…The stability and safety of materials represent critical issues in engineering structures, where the presence of cracks may jeopardize the strength of materials. Many researchers have been drawn to investigate the stability behavior of structures or materials subject to remote stress by considering the types of materials such as infinite [1][2][3], finite [4,5], half plane [6][7][8], and bonded materials [9][10][11][12][13]. These types of materials have several conditions such as elasticity [14][15][16], thermoelasticity [17][18][19], magnetoelasticity [20][21][22], and electricity [23][24][25].…”