A Modified Strain-displacement Method for High Accuracy 8-Node Solid Finite Element

Abstract

Higher-order three-dimensional solid elements are widely used for machine design and structural analyses. Although higher-order solid elements offer higher accuracy, the assembly routines often consume large amount of computational time and memory usage. In contrast, lower-order solid elements such as an 8-nod are simpler in programming implementation and consume less computational resources. However, they can produce problems of locking phenomena e.g. membrane and shear locking. Moreover, in a three-dimensional analysis using continuum solid elements, it is necessary to consider the stresses in the through-thickness direction, for example, in layered soil and foundation. This research aims to develop a modified strain-displacement finite element formulation that eliminates locking problems and generally applicable to both thick and thin threedimensional structures. The proposed formulation is based on the key concept of energy equivalence mapped between the global and natural curvilinear coordinates. The advantage of the proposed method is the ability to select a set of chosen strain functions that can be defined arbitrarily on the natural curvilinear coordinates.