Trefftz Finite Element Method and Its Applications

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An unsymmetric 4‐node, 8‐DOF plane membrane element perfectly breaking through MacNeal's theorem (2015, methodology): “The basic analytical solutions in terms of second form of quadrilateral area coordinate method (QACM-II) for pure bending Just as the Trefftz finite element method [54] and the hybrid stress-function element method proposed recently [55–60], the fundamental analytical solutions of governing equation”
A new special element for stress concentration analysis of a plate with elliptical holes (2012, background): “For a well-posed plane linear elastic problem occupying the domain , the corresponding partial differential governing equations consist of [16] Equilibrium equations Lσ + b = 0, (1)”