Vuong-Dieu Trinh, Farid Abed-Meraim* and Alain Combescure
The Journal of Mechanical Science and Technology, vol. 25, no. 9, pp.2345-2364, 2011

Abstract : This paper presents the development of a new prismatic solid–shell finite element, denoted SHB6, obtained using a purely threedimensional approach. This element has six nodes with displacements as the only degrees of freedom, and only requires two integration points distributed along a preferential direction, designated as the “thickness”. Although geometrically three-dimensional, this element can be conveniently used to model thin structures while taking into account the various phenomena occurring across the thickness. A reduced integration scheme and specific projections of the strains are introduced, based on the assumed-strain method, in order to improve performance and to eliminate most locking effects. It is first shown that the adopted in-plane reduced integration does not generate “hourglass” modes, but the resulting SHB6 element exhibits some shear and thickness-type locking. This is common in linear triangular elements, in which the strain is constant. The paper details the formulation of this element and illustrates its capabilities through a set of various benchmark problems commonly used in the literature. In particular, it is shown that this new element plays a useful role as a complement to the SHB8PS hexahedral element, which enables one to mesh arbitrary geometries. Examples using both SHB6 and SHB8PS elements demonstrate the advantage of mixing these two solid–shell elements.

Keyword : Assumed-strain solid–shell SHB6; Benchmark problems; Buckling; Hourglass; Shear and thickness locking; Six-node prism