TY - EJOU
AU - Dong, L.
AU - Atluri, S. N.
TI - Development of T-Trefftz Four-Node Quadrilateral and Voronoi Cell Finite Elements for Macro- \& Micromechanical Modeling of Solids
T2 - Computer Modeling in Engineering \& Sciences
PY - 2011
VL - 81
IS - 1
SN - 1526-1506
AB - In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed fields at the boundary and in the interior, are enforced alternatively, using a two-field boundary variational principle, collocation, and the least squares method. The corresponding four-node quadrilateral elements with/without drilling degrees of freedom are developed, for modeling macrostructures of solids. These three approaches are also used to derive T-Trefftz Voronoi Cell Finite Elements (VCFEM), for micromechanical analysis of heterogeneous materials. Several two dimensional macro- & micromechanical problems are solved using these elements. Computational results demonstrate that the elements derived using the collocation method are very simple, accurate and computationally efficient. Because the elements derived by this approach are also not plagued by LBB conditions, which are almost impossible to be satisfied a priori, we consider this class of elements to be useful for engineering applications in micromechanical modeling of heterogeneous materials.
KW - T-Trefftz
KW - finite element
KW - variational principle
KW - collocation
KW - least squares
KW - LBB conditions
KW - drilling degree of freedom
KW - VCFEM
DO - 10.3970/cmes.2011.081.069