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Energy methods and finite element techniques : stress and vibration applications /
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
Elsevier,
[2022]
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover
- Energy Methods and Finite Element Techniques
- Copyright Page
- Contents
- About the authors
- Preface
- I. Energy Method
- 1 Fundamentals of energy methods
- 1.1 Principles of virtual work (P.V.W.)
- 1.2 Work function and potential energy
- 1.3 Total potential energy
- 1.4 Application of P.V.W. to generate differential equations for axial member
- 1.5 Principles of stationary total potential energy (P.S.T.P.E.) and trigonometric series for beam bending
- 1.6 Principle of virtual complementary energy (P.V.C.E.)
- 1.6.1 Castiglianon's theorem of deflections
- 1.7 Torsion of a rectangular section bar
- Problems
- Bibliography
- 2 Direct methods
- 2.1 Galerkin method (G.M.)
- 2.1.1 Boundary value problems
- 2.1.2 Assessment of accuracy
- 2.2 Rayleigh ritz method (R.R.M.)
- 2.3 Examples using the P.S.T.P.E. with non-trigonometric coordinate functions
- 2.4 Case studies for bar and beam problems under different loading and support conditions
- 2.4.1 Bar problem by Galerkin's method using polynomial assumption
- 2.4.2 Beam under uniformly distributed load by using a higher order polynomial deflected shape
- 2.4.3 Cantilever beam under uniformly varying load
- 2.4.4 A cantilever beam under a concentrated load at the free end
- 2.4.5 Torsion of rectangular section using G.M
- 2.4.6 Application of energy methods to Lambda frame
- Problems
- 3 Application of energy methods to plate problems
- 3.1 Plate bending
- 3.2 Plate stretching
- 3.3 Buckling of thin plates using energy method
- 3.3.1 Inelastic buckling
- 3.3.2 Pure shear
- 3.4 Application of Galerkin's method G.M. to plate bending
- 3.5 Kantorovich method
- 3.6 Application of Kantorovich's method to plate bending
- Problems
- Bibliography
- 4 Energy methods in vibrations
- 4.1 Rayleigh's method
- 4.2 Rayleigh's energy theorem (R. Principle).
- 4.3 Rayleigh Ritz method (modified Ritz method)
- 4.4 Plate applications
- 4.4.1 Rayleigh's method
- 4.4.2 Ritz method
- 4.4.3 Galerkin-Vlasov method
- 4.5 Application to the governing differential equation of plates
- 4.5.1 Rayleigh-Ritz
- 4.5.2 Galerkin's method
- Problems
- Bibliography
- II. Finite Element Method
- 5 Introduction to finite element method: bar and beam applications
- 5.1 Bar extension
- 5.2 Equivalent nodal forces of the axially distributed loading
- 5.3 Temperature effects-application to axially loaded problems
- 5.4 Application to the beam bending
- 5.5 Inclined bar element
- Problems
- Bibliography
- 6 Two-dimensional problems: application of plane strain and stress
- 6.1 Two-dimensional modeling: triangular elements
- 6.1.1 Constant strain triangle element
- 6.1.2 Loading conditions
- 6.2 Derivation of the 4-node quadrilateral element, formulation of the element equations
- 6.3 Parallelogramic element
- Problems
- Bibliography
- 7 Torsion problem
- 7.1 Total potential energy
- 7.2 Iso-parametric formulation of torsion problem: triangular element
- Problems
- Bibliography
- 8 Axisymmetric elasticity problems
- 8.1 Geometrical description
- 8.2 Three nodes triangular element
- 8.3 Representation of the applied forces as an equivalent nodal forces
- 8.3.1 Body force
- 8.3.2 Rotating bodies
- 8.3.3 Surface traction
- Problems
- Bibliography
- 9 Application of finite element method to three-dimensional elasticity problems
- 9.1 Three-dimensional elasticity relations
- 9.2 8-Node hexahedral element
- 9.3 Steps of formulation
- 9.4 Example of parallelopiped element
- 9.5 Tetrahedron element
- 9.5.1 Element description and element stiffness [k]e determination
- 9.5.2 Equivalent nodal forces
- 9.5.3 System stiffness and load vector
- Problems
- Bibliography.
- 10 Application of finite element to the vibration problems
- 10.1 General
- 10.2 Application to axial vibration of a bar
- 10.3 Equation of motion
- 10.3.1 Mode shapes determination
- 10.3.2 Orthogonality of mode of vibration
- 10.4 Application to transverse vibration of beams
- 10.5 Constant strain element
- 10.6 Quadrilateral elements
- 10.7 Axisymmetric triangular element
- 10.8 Consistent element mass matrix for the 8-nodes solid element
- 10.9 Consistent mass matrix for a tetrahedron element
- Problems
- Bibliography
- 11 Steady state heat conduction
- 11.1 Steady-state heat flows
- 11.2 Boundary conditions
- 11.3 Derivation of equilibrium equations
- 11.4 Application of three nodes constant strain triangular element
- 11.4.1 Determination of heat conduction matrices [k]cond
- 11.4.2 Determination of boundary convection matrix
- 11.4.3 Determination of boundary convection vector Qcv
- 11.4.4 Determination of applied heat vector Qb
- 11.4.4.1 Heat conduction matrices determination
- 11.4.4.2 Convection matrix determination
- 11.4.4.3 Determination of heat flow
- 11.5 4-Node quadrilateral element
- Problems
- Bibliography
- 12 Shape function determinations and numerical integration
- 12.1 One-dimensional formulations
- 12.1.1 Polynomial assumption
- 12.1.2 Lagrange interpolation
- 12.2 Two-dimensional applications
- 12.2.1 Triangular element
- 12.2.2 Shape functions in terms of area coordinates
- 12.2.3 Interpolation formula-quadrilateral elements
- 12.2.4 9-Node Lagrangian element
- 12.2.5 12-Node serendipity element
- 12.2.6 8-Node serendipity element
- 12.2.7 Superposition theory
- 12.3 Convergence criteria
- 12.4 Three dimensions of pentahedral element
- 12.4.1 Intrinsic 6-node element
- 12.4.2 Natural coordinates
- 12.4.3 Higher-order element: the 15-node serendipity element.
- 12.4.4 18-Node Lagrangian element
- 12.4.5 Serendipity elements
- 12.4.6 Tetrahedral elements
- 12.4.6.1 4-Node tetrahedral element
- 12.4.6.2 Higher-order elements in terms of volume coordinates
- 12.5 Numerical integration
- 12.5.1 Gaussian quadrature formula
- 12.5.2 Newton's _Cotes quadrature rule
- 12.5.3 Gauss-Legendre quadrature
- 12.5.4 Arithmetic evaluation
- 12.5.5 Numerical integration in 2D
- 12.5.6 Integration in triangular numerical
- 12.5.7 Numerical integration in 3D elements
- Problems
- Bibliography
- 13 Higher-order isoparametric formulation
- 13.1 Isoparametric element-thin plate bending element
- 13.1.1 8-Node isoparametric element
- 13.1.2 Strain-displacement relationship [B]
- 13.1.2.1 Element stiffness matrix
- 13.1.2.2 Element mass matrix
- 13.1.2.3 Equivalent nodal forces
- 13.1.3 Assembly of system equations
- 13.1.4 Strain and stress calculations
- 13.2 General shell element
- 13.3 Axisymmetric solid under axisymmetric loading
- 13.4 Laminated composite plates
- 13.4.1 Stress-strain relations for anisotropic material
- 13.4.2 Stress-strain relations for plate bending in an orthotropic
- 13.4.3 Strain and stress variations in a lamina
- 13.4.4 Resultant laminate forces and moments
- 13.4.5 Symmetric laminate
- 13.4.6 Antisymmetric laminates
- 13.4.6.1 Antisymmetric cross-ply laminates
- 13.4.6.2 Antisymmetric angle-ply laminates
- 13.4.7 Higher shear deformation theory
- 13.4.8 F.E. modeling using the 9-node Lagrangian quadrilateral isoparametric element
- 13.4.8.1 Formulation
- 13.4.8.2 Element stiffness matrix [k]e
- 13.4.8.3 Element mass matrix [m]e
- Problems
- Bibliography
- 14 Finite element program structures
- 14.1 Introduction
- 14.2 Structure of the F.E. process, static analysis
- 14.3 Flow chart of the subroutine input's DATA.
- 14.4 Flow chart of the subroutine shape functions and their derivatives
- 14.5 Flow chart of the Jacobian matrix subroutine
- 14.6 Flow chart of the subroutine [BM] matrix
- 14.7 Flow chart of subroutine [DM]
- 14.8 Flow chart of subroutine [DM]�[BM]
- 14.9 Flow chart of the element stiffness matrix subroutine [K] of size (NDFE, NDFE)
- 14.10 Flow chart of the assembly subroutine of the global stiffness matrix [KG]
- 14.11 Global load vector [FG]
- 14.11.1 Flow chart of the subroutine parabolic
- 14.11.2 Flow chart of uniform pressure subroutine
- 14.11.3 Flow chart of the body force subroutine
- 14.11.4 Flow chart of the concentrated loading subroutine
- 14.11.5 Flow chart of the thermal loading
- 14.12 Application of BCs flow chart
- 14.13 Flow chart solution subroutine
- 14.14 Calculation of stresses
- 14.15 Element mass matrix
- 14.16 Free vibration
- Bibliography
- Appendix A: Review of typical framed structure 2-node elements
- A.1 Continuous beam element
- A.2 Plane truss element
- A.3 Plane frame element
- A.4 Grid element
- A.5 Space truss element
- A.6 Space frame element
- A.7 Rotating shaft element
- A.8 Torque rod element
- Appendix B: Penalty function
- Summary: Elimination Approach
- Appendix C: Analytical solution of equations of motion
- C.1 Uncoupled equations of motion of undamped problems
- Appendix D: Numerical integration in time-dependent problems
- Index
- Back Cover.