Hybrid-trefftz quadrilateral elements for thick plate analysis

Alternative T‐complete systems of shape functions applied in analytical Trefftz finite elements

“…However, it should be noted that, in all the examples carried out by the authors, the range of acceptable final results was broader than the range of stable e K . Relative solution error (21) and relative measure of generalized energy density error (22) with its average value…”

Mixed types of boundary conditions at corners of linear elastostatics and their numerical solutions

“…More importantly, based on the explicit particular solutions of corners given in [1,2] and this paper, we may develop a number of efficient (even new) numerical methods for linear elastostatics, such as the combined method in [9][10][11][12][13], and the Trefftz methods [14][15][16], which include the boundary approximate method [10], the collocation Trefftz method [17,18], the hybrid Trefftz method (see [19][20][21][22][23][24][25]8]), the boundary collocation techniques [26], etc. This paper is organized as follows.…”

Two efficient hybrid-trefftz elements for plate bending analysis

“…By inserting the formula (21) into the equation (20) and simplifying it, the governing equations of thick plate are obtained in the following appearance [22]:…”

“…To find the homogeneous solution for the equation (3), Petrolito supposed θ x and θ y in the following manner [22]:…”

“…Because of high accuracy and efficiency, this technique soon caught the attention of other researchers as well. The mentioned approach has been successfully utilized in solving plane elasticity problems [9,32], thin plates [14,19], Reissner-Mindlin plates [7,13,22], shells [24], Helmholtz problem [33], heat conduction [10], contact problems [26], and three-dimensional structures [21]. In 1995, Jirousek and his colleagues presented a family of quadrilateral hybrid-Trefftz (HT) p-elements for moderately thick plates [16].…”