tailieunhanh - Ebook The finite element method: Part 2
(BQ) Part 2 book "The finite element method" has contents: FEM for plates and shells, FEM for 3D solids, special purpose elements, modelling techniques, FEM for heat transfer problems, using ABAQUS. | 8 FEM FOR PLATES AND SHELLS INTRODUCTION In this chapter, finite element equations for plates and shells are developed. The procedure is to first develop FE matrices for plate elements, and the FE matrices for shell elements are then obtained by superimposing the matrices for plate elements and those for 2D solid plane stress elements developed in Chapter 7. Unlike the 2D solid elements in the previous chapter, plate and shell elements are computationally more tedious as they involve more Degrees Of Freedom (DOFs). The constitutive equations may seem daunting to one who may not have a strong background in the mechanics theory of plates and shells, or the integration may be quite involved if it is to be carried out analytically. However, the basic concept of formulating the finite element equation always remains the same. Readers are advised to pay more attention to the finite element concepts and the procedures outlined in developing plate and shell elements. After all, the computer can handle many of the tedious calculations/integrations that are required in the process of forming the elements. The basic concepts, procedures and formulations can also be found in many existing textbooks (see, . Petyt,1990; Rao, 1999; Zienkiewicz and Taylor, 2000; etc.). PLATE ELEMENTS As discussed in Chapter 2, a plate structure is geometrically similar to the structure of the 2D plane stress problem, but it usually carries only transversal loads that lead to bending deformation in the plate. For example, consider the horizontal boards on a bookshelf that support the books. Those boards can be approximated as a plate structure, and the transversal loads are of course the weight of the books. Higher floors of a building are a typical plate structure that carries most of us every day, as are the wings of aircraft, which usually carry loads like the engines, as shown in Figure . The plate structure can be schematically represented by its middle plane laying on the x–y .
đang nạp các trang xem trước
