Finite Element Method

- Physics and Solution Methods

  • Format
  • Bog, paperback
  • Engelsk

Beskrivelse

Finite Element Method: Physics and Solution Methods aims to provide the reader a sound understanding of the physical systems and solution methods to enable effective use of the finite element method. This book focuses on one- and two-dimensional elasticity and heat transfer problems with detailed derivations of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. Following the chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing partial differential equation is defined over a subsegment (element) of the solution domain. As well as being a guide to thorough and effective use of the finite element method, this book also functions as a reference on theory of elasticity, heat transfer, and mechanics of beams.

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Detaljer
Størrelse og vægt
  • Vægt290 g
  • coffee cup img
    10 cm
    book img
    15,2 cm
    22,9 cm

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    Stress Radiation Stability Convection Convergence Calculus of variations Pascal's triangle Numerical integration Conduction Simulation Form Mapping Domain Jacobian Consistency Boundary value problem Boundary conditions Equation of Motion Radiation heat transfer Constitutive relations Initial Value Problem Boundary Weak Galerkin's Method Accuracy Plane Stress Euler's method Déformation Modelling Two-dimensional Penalty Method Coordinate transformation Lagrange interpolation Timoshenko beam One-dimensional C(0) interpolation Differential area CST element Equation of motion of an elastic bar Crank–Nicholson method Finite element form of a boundary value problem Equation of equilibrium Essential and natural boundary conditions for one-dimensional heat transfer Consistent nodal forces force Finite difference formulas Finite element analysis of two-dimensional frames Implementation of boundary conditions Initial stress/strain Element assembly Linear elastic materials Essential and natural boundary conditions for two-dimensional heat transfer Element connectivity table Excessive stiffness Fourier's law of heat conduction linear interpolation Generalized trapezoidal method Mesh Convergence Method of weighted residuals Gauss quadrature Plane Strain Isoparametric elements Q9 element Stress transformations Strain compatibility conditions Strong form Time discretization of heat transfer equation Spurious shear strain Total Potential Energy strain Semidiscrete heat transfer equation Thermal stress/strain Minimum total potential energy principle Principle stresses Q4 Element Monotonic convergence Shape Function Rayleigh–Ritz finite element method Steady State Heat Transfer Q6 element Quadratic interpolation Uniaxial deformation thermal loads Transient Heat Transfer Two-dimensional polynomial interpolation Unit tangent and normal vectors

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