tailieunhanh - A new prismatic solid-shell element ‘SHB6’: Assumed-strain formulation and evaluation on benchmark problems

In this paper, the formulation of a new six-node solid–shell element denoted (SHB6) is proposed. This prismatic element is based on a purely three-dimensional approach, and hence has displacements as the only degrees of freedom. A reduced integration scheme is adopted consisting of one-point in-plane quadrature and an arbitrary number of integration points, with a minimum number of two, distributed along the ‘thickness’ direction. | Vietnam Journal of Mechanics, VAST, Vol. 31, No. 4 &0 (2009), pp. 279 – 292 A NEW PRISMATIC SOLID-SHELL ELEMENT ‘SHB6’: ASSUMED-STRAIN FORMULATION AND EVALUATION ON BENCHMARK PROBLEMS Vuong-Dieu Trinh1 , Farid Abed-Meraim1 , Alain Combescure2 1 LPMM UMR CNRS 7554, Arts et Métiers ParisTech, 4 rue Augustin Fresnel, 57078 Metz 2 LaMCoS UMR CNRS 5259, INSA-Lyon, 18, 20 rue des Sciences, 69621 Villeurbanne, France Abstract. In this paper, the formulation of a new six-node solid–shell element denoted (SHB6) is proposed. This prismatic element is based on a purely three-dimensional approach, and hence has displacements as the only degrees of freedom. A reduced integration scheme is adopted consisting of one-point in-plane quadrature and an arbitrary number of integration points, with a minimum number of two, distributed along the ‘thickness’ direction. Moreover, in order to enhance its performance and to greatly reduce most locking effects, specific projections are introduced based on the assumed-strain method. The resulting derivation can then be used to model thin structural problems, while taking into account the various through-thickness phenomena. A careful analysis of potential stiffness matrix rank deficiencies reveals that no hourglass modes need to be controlled. However, without assumed-strain method, the element exhibits some shear and thickness-type locking, which is common in linear triangular elements associated with constant strain states. After the formulation of the element is detailed, its performance is assessed through a set of representative benchmark problems illustrating its capabilities in various situations. More specifically, this prismatic solid–shell element proves to be an essential complement to the SHB8PS hexahedral element in meshing arbitrarily complex geometries. Keywords. solid–shell element shb6, shear and thickness locking, assumed-strain method, hourglass modes, benchmark problems. 1. INTRODUCTION Accuracy and efficiency of finite