A general degree semihybrid triangular compatible finite element formulation for Kirchhoff plates

Abstract

Summary We revisit compatible finite element formulations for Kirchhoff plates and propose a new general degree hybridized approach that strictly imposes C1 continuity. These new elements are triangular and based on nodal polynomial approximation functions that only use displacement and rotation degrees of freedom for assembly, and thereby “nearly” impose C1 continuity. This condition is then strictly enforced by adding appropriately chosen hybrid constraints and the corresponding Lagrange multipliers. Unlike all other existing approaches, this formulation allows for the definition of elements of arbitrary degree considering a single polynomial basis for each element, without using degrees of freedom associated with second‐order derivatives. The convergence is compared with that of alternative approaches in terms of numbers of elements and degrees of freedom.

Two families of two‐dimensional finite element interpolation functions of general degree with general continuity

“…The recently proposed general‐degree semi‐hybrid compatible formulation for Kirchhoff plates 14 uses the function and some first derivatives as nodal variables, which impose “as much as possible” $$$ {C}^1 $$$ continuity on triangular elements. To enforce strict compatibility, while avoiding the use of second derivatives, additional (hybrid) constraints have to be imposed on the sides of the elements.…”

Representing capabilities of novel semi-analytical triangular plate elements

“…Besides, the shear forces correspond to the integrals of the out-of-plane shear stresses and could be calculated as follows. 43…”