Finite Element Analysis. Barna Szabó

9 Non‐linear models 9.1 Heat conduction 9.2 Solid mechanics 9.3 Chapter summary Notes

      17  Appendix A: Appendix ADefinitionsDefinitions A.1 Normed linear spaces, linear functionals and bilinear forms A.2 Convergence in the space A.3 The Schwarz inequality for integrals Notes

      18  Appendix B: Appendix BProof of h‐convergenceProof of h‐convergence

      19  Appendix C: Appendix CConvergence in 3D: Empirical resultsConvergence in 3D: Empirical results

      20  Appendix D: Appendix DLegendre polynomialsLegendre polynomials D.1 Shape functions based on Legendre polynomials

      21  Appendix E: Appendix ENumerical quadratureNumerical quadrature E.1 Gaussian quadrature E.2 Gauss‐Lobatto quadrature Note

      22  Appendix F: Appendix FPolynomial mapping functionsPolynomial mapping functions F.1 Interpolation on surfaces

      23  Appendix G: Appendix GCorner singularities in two‐dimensional elasticityCorner singularities in two‐dimensional elasticity G.1 The Airy stress function G.2 Stress‐free edges Notes

      24  Appendix H: Appendix HComputation of stress intensity factorsComputation of stress intensity factors H.1 Singularities at crack tips H.2 The contour integral method H.3 The energy release rate Note

      25  Appendix I: Appendix IFundamentals of data analysisFundamentals of data analysis I.1 Statistical foundations I.2 Test data I.3 Statistical models I.4 Ranking I.5 Confidence intervals Notes

      26  Appendix J: Appendix JEstimation of fastener forces in structural connectionsEstimation of fastener forces in structural connections

      27  Appendix K: Appendix KUseful algorithms in solid mechanicsUseful algorithms in solid mechanics K.1 The traction vector K.2 Transformation of vectors K.3 Transformation of stresses K.4 Principal stresses K.5 The von Mises stress K.6 Statically equivalent forces and moments Notes

      28  Bibliography

      29  Index

      30  End User License Agreement

      List of Tables

      1 Chapter 1Table 1.1 Local and global numbering in Example 1.6.Table 1.2 Exact values of the potential energy for

,

and

.Table 1.3 Example: Computed and estimated values of the potential energy

. Un...Table 1.4 Example: Element‐by‐element and total relative errors in energy nor...Table 1.5 Example: Element‐by‐element and total relative errors in energy nor...Table 1.6 Example:p‐Convergence of the 24th eigenvalue in Example 1.16.Table 1.7 The computed values of

.

      2 Chapter 2Table 2.1 Exercise 2.30: Boundary conditions

      3 Chapter 3Table 3.1 Example 3.3. Nodal forces (kN). The notation is shown in Fig. 3.12(...Table 3.2 Example 3.3. Nodal forces (kN). Solution on the shaded domain shown...

      4 Chapter 4Table 4.1 L‐shaped domain, radical mesh (

), 27 elements, product space. Esti...Table 4.2 L‐shaped domain, radical mesh (