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In this paper, a new finite element method, termed the generalized modal element method (GMEM), is proposed. In GMEM, the element stiffness is derived by decomposing element deformation patterns into individual element generalized modes, where different methods are used to construct the generalized modes. Specifically, three different modal construction methods, including analytical method, assumed displacement method and traditional finite element technique, are proposed for developing the element generalized modes. The concept of modal local coordinate systems is also proposed to ensure the element frame invariance when using polynomial displacement functions, which successfully enables one to use the analytical solutions derived from governing differential equations to develop high accuracy element formulations. An asymmetric hexahedral solid element and a symmetric hexahedral solid element are subsequently derived by using GMEM. The displacement functions of the elemental 24 generalized modes are expressed in terms of Cartesian coordinates so that the element behavior is independent of mesh distortions. Furthermore, the first 21 generalized modes are derived from analytical method making the element capable of avoiding common locking phenomena. Several benchmark problems are performed to demonstrate the accuracy and performance of the new element formulations in linear static and frequency analysis. [ABSTRACT FROM AUTHOR]

In this paper, two eight-node asymmetric solid-shell elements are firstly presented to illustrate the use of traditional finite element technique in GMEM for constructing new finite element formulations. In these two elements, the analytical method is utilized to derive the displacement functions of the basic in-plane modes, which makes the resulted elements free of mesh distortions for these modes. For out-of-plane modes, the Mindlin plate elements CQUAD4 and QTS4 are integrated to calculate the corresponding modal displacement vectors and modal force vectors of solid-shell elements. As a result, the displacement functions of the plate-bending element range up to three orders of magnitude. On the other hand, since the asymmetric elements cannot be applied to frequency analysis, two symmetric solid-shell elements are proposed by using a modal transformation method, in which the in-plane modes are derived from the previous proposed symmetric solid element S-MEM8S and the out-of-plane modes are constructed by plate elements CQUAD4 and QTS4, respectively. Various benchmarks including linear static and frequency analysis are presented to demonstrate the accuracy and efficiency of the presented elements. [ABSTRACT FROM AUTHOR]