TAILIEUCHUNG - Ebook The finite element methods111

| 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 .

• Cơ khí - Chế tạo máy
• The finite element methods
• The time finite element methods
• The shape functions of an axial finite bar
• Axial finite bar
• Finite element methods
• Time finite element
• Non linear axial bar element
• Vietnam Journal of Mechanics
• Locking phenomena in finite element analysis
• Deep beam and removal method
• Finite element analysis
• Exhibit slow convergence
• Dynamic calculation for lathe body system
• Design parameters and external forces were changed values
• CosMosDesign software of Finite element methods
• The finite element method
• Come mechanical manufacture centers
• Finite element method
• Historical introduction
• Weighted residual
• Variational methods
• Elliptic problems
• Lecture Finite element method
• Bài giảng Phương pháp phần tử hữu hạn
• Methods of Weighted Residuals
• Generalized displacements
• Vibration analysis
• Preprocessing a static finite elements simulation
• Transtibial prosthesis using cae tools
• The Charges present during competition
• Finite element analysis methods
• Coupled finite discrete element modeling
• Potential applications in civil engineering
• Numerical methods
• Coupling methods
• Civil engineering applications
• An enforced essential boundary condition BV penalty method
• The element free galerkin (EFG) methods
• Two dimensional problem
• Computational fluid dynamics
• CFD techniques
• partial differential equations
• basic theoretical
• algorithmic aspects
• Metal machining
• Theory and applications
• Applications of finite element analysis
• Process selection
• Improvement and control
• Higher order elements
• The isoparametric concept
• Numerical Investigations
• Characterization
• Continuum Mecha
• Problem Domain
• Finite Volume Methods
• Compressible high speed gas flow
• Shallow water problems
• Computer implementation of the CBS algorithm
• Multigrid methods
• Ordinary Differential Equations
• Mathematical Software
• Piecewise Polynomial Functions
• One Space Variable
• Governing equations
• Linear problems
• Introduction to finite element methods
• Miscellaneous weighted residual methods
• Static analysis of reissner mindlin plates
• ES+NS MITC3 elements
• The smoothed finite element methods
• The shear locking phenomenon
• Thick plates the ES+NS MITC3 element
• Multiresolution Approximation
• Mathematically Founded Design
• HeterogeneousMathematicalModels
• Fluid Dynamics
• Associated Solution Algorithms
• Theory of elasticity
• Incompressible materials
• The Uzawa algorithm
• Iterative methods
• Systems of linear algebraic equations
• Nodal points
• Nodal basis functions
• p adaptive finite elements
• Systematically define
• Quadratic elements
• Tạp chí Khoa học và Công nghệ
• Central difference method
• Newmark’s constant average acceleration method
• Newmark’s linear acceleration method
• Input output (I O)
• Multitasking
• Misconceptions
• Further topics
• Hardware