TAILIEUCHUNG - Ebook The finite element method (Volume 1: The basis - 5th edition): Part 2

(BQ) Part 2 book "The finite element method (Volume 1: The basis)" has contents: Adaptive finite element refinement; the time dimension - semi-discretization of field and dynamic problems and analytical solution procedures; couple systems; computer procedures for finite element analysis,.and other contents. | 12 Incompressible materials, mixed methods and other procedures of solution Introduction We have noted earlier that the standard displacement formulation of elastic problems fails when Poisson's ratio becomes or when the material becomes incompressible. Indeed, problems arise even when the material is nearly incompressible with > 0:4 and the simple linear approximation with triangular elements gives highly oscillatory results in such cases. The application of a mixed formulation for such problems can avoid the di culties and is of great practical interest as nearly incompressible behaviour is encountered in a variety of real engineering problems ranging from soil mechanics to aerospace engineering. Identical problems also arise when the ¯ow of incompressible ¯uids is encountered. In this chapter we shall discuss fully the mixed approaches to incompressible problems, generally using a two-®eld manner where displacement (or ¯uid velocity) u and the pressure p are the variables. Such formulation will allow us to deal with full incompressibility as well as near incompressibility as it occurs. However, what we will ®nd is that the interpolations used will be very much limited by the stability conditions of the mixed patch test. For this reason much interest has been focused on the development of so-called stabilized procedures in which the violation of the mixed patch test (or BabusÏ ka±Brezzi conditions) is arti®cially compensated. A part of this chapter will be devoted to such stabilized methods. Deviatoric stress and strain, pressure and volume change The main problem in the application of a `standard' displacement formulation to incompressible or nearly incompressible problems lies in the determination of the mean stress or pressure which is related to the volumetric part of the strain (for isotropic materials). For this reason it is convenient to separate this from the total stress ®eld and treat it as an independent variable. Using the `vector'

• Cơ khí - Chế tạo máy
• The finite element method
• Adaptive finite element refinement
• The time dimension
• Couple systems
• Finite element analysis
• Computer procedures
• Further topics
• The boundary element method
• Computational aspects
• Lecture Finite element method
• Finite element method
• Basis equation of plane problem
• Finite element discretization
• Quadrilateral plane element
• Triangular plane element
• Introduction to the finite element method
• Finite element equations
• Heat transfer
• Fem for solid mechanics problems
• Finite elements
• The finite element method in engineering
• Interpolation models
• Isoparametric elements
• System equations
• Introduction to mechanics
• Fundamentals for finite element method
• FEM for beams
• FEM for frames
• FEM for Two Dimensional solids
• Finite element method using MATLAB
• CRC Mechanical engineering series
• Approximation techniques
• Finite element programming
• Direct approach
• Vietnam Journal of Mechanics
• Smoothed finite element method
• Two dimensional elasto plasticity
• The finite element
• The smoothed finite element method
• Mesh distortion and volumetric locking
• The isoparametric concept
• Higher order elements
• Locking phenomena in finite element analysis
• Deep beam and removal method
• Exhibit slow convergence
• Finite Element Methods
• Bài giảng Phương pháp phần tử hữu hạn
• Stiffness method
• Stiffness matrix
• Boundary conditions
• Lecture Structural analysis
• Finite element
• Structural analysis
• Finite element approach
• Element approach
• A first course in the finite element method
• Introduction to the stiffness method
• Development of truss equations
• Development of beam equations
• The plane stress
• Numerical method
• Electro Magnetic analysis
• Thermal analysis
• Axisymmetric elements
• Isoparametric formulation
• Three dimensional stress analysis
• Plate bending element
• Vibrational principles
• Galerkin approximation
• Partial differential equations
• Isoparametric finite elements
• Historical introduction
• Weighted residual
• Variational methods
• Elliptic problems
• Heat and fluid flow
• Some basic discrete systems
• Steady state heat conduction
• Transient heat conduction analysis
• Truss structures
• Elasticity problem
• Basic equations
• Solution procedure
• Three dimensional problems
• Dynamic analysis
• Cast3m implementation of the extended finite element method
• The extended finite element method for cohesive crack
• Quasi brittle materia
• The proposed implementation
• The displacement discontinuities
• The node based smoothed finite element method
• Free vibration problems
• The proposed formulation
• No spurious non zero energy modes
• Science and technology development
• Extended finite element method
• Simulating the mechanical behavior
• Multiple random holes and inclusions
• Functionally graded material
• The finite element method software
• Tạp chí khoa học và công nghệ
• Modeling the mechanical behavior
• Functionally graded material plates with multiple random inclusions
• Modeling of electromagnetic force
• Magnetic vector potential formulation via
• Sbproblem finite element method
• Subproblem finite element method
• Magnetic vector potential formulation