A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis

Trefftz polygonal finite element for linear elasticity: convergence, accuracy, and properties

“…This can be used to generate hybrid finite elements. Earlier studies employed boundary-type approximation associated with Trefftz to develop special type finite elements, for example, elements with holes/ voids [35,36], for plate analysis [37][38][39]. Recently, the idea of employing local solutions over arbitrary finite elements has been investigated in [5,[31][32][33].…”

T‐complete functions for thin and thick plates on elastic foundation

“…This can be shown with very simple examples (bar under tension), as presented in the monograph by Cook et al [1]. More complex examples (Reissner-Mindlin plate) presented by Jirousek et al [2] illustrate the consequences of using a set of incomplete trial functions. Depending on the boundary conditions, the results may diverge, converge to a solution close to the exact solution or converge to the exact solution.…”

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

“…Different radius to thickness ratios have been considered, namely thick plate (R/t=10), thin plate (R/t=100) and very thin plate (R/t=1000), respectively. The reference solutions are based on classical Kirchhoff theory for thin plates, or Reissner-Mindlin theory for thick plates as quoted in (Timoshenko et al, 1959) and (Jirousek et al, 1995). The normalized deflections at points O, D, E and F are reported in Table 13 for different meshes and radius to thickness ratios, R/t.…”

“…The reference solutions for thin plates are based on Kirchhoff theory as quoted in (Timoshenko et al, 1959); for thick plates, they are taken from (Jirousek et al, 1995). Table 14 summarizes the normalized results for the central deflection with different meshes and span to thickness ratios, L/t.…”