| Description |
1 online resource |
| Contents |
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) |
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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 |
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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 |
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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 |
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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 |
| Notes |
Includes index |
| Subject |
Structural dynamics.
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Strains and stresses.
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Finite element method.
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stress.
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strain.
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Finite element method
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Strains and stresses
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Structural dynamics
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| Form |
Electronic book
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| Author |
Al-Waily, Muhannad, author
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Resan, Kadhim Kamil, author
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| ISBN |
9780323886512 |
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0323886515 |
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