Читать книгу Finite Element Analysis - Barna Szabó - Страница 4

1 Chapter 1Figure 1.1 Exact and approximate solutions for the problem in Example 1.1.Figure 1.2 Exercise 1.3: The function .Figure 1.3 Lagrange shape functions in one dimension, .Figure 1.4 Legendre shape functions in one dimension, .Figure 1.5 Typical finite element basis functions in one dimension.Figure 1.6 Recommended choice of the function in one dimension.Figure 1.7 Example 1.9. Values of computed by the direct method.Figure 1.8 Exercise 1.18. Notation.Figure 1.9 Relative error in energy norm. , .Figure 1.10 Relative error in energy norm. , .Figure 1.11 The solution , given by eq. (1.119), in the neighborhood of f...Figure 1.12 The exact solution for and its linear interpolant for , unifo...Figure 1.13 The ratio corresponding to the h version, .Figure 1.14 The ratio corresponding to the p version. Uniform mesh, 5 elem...

2 Chapter 2Figure 2.1 Control volume and notation for heat conduction.Figure 2.2 Notation for Example 2.2.Figure 2.3 Example 2.3: The solution u of (a) the periodic problem, (b) the ...Figure 2.4 Notation for two‐dimensional domains.Figure 2.5 Example 2.4: The solution domain and finite element mesh (mm).Figure 2.6 Control volume and notation for heat conduction in 2D.Figure 2.7 Notation for stress components.Figure 2.8 Spring boundary condition. Schematic representation.Figure 2.9 Symmetry and antisymmetry of vectors in two dimensions.Figure 2.10 Notation.Figure 2.11 Virtual displacements corresponding to (a) σ ₁₁ and (b) σ...Figure 2.12 Rigid body constraints. Notation.Figure 2.13 Example 2.7. NotationFigure 2.14 Notation.Figure 2.15 Notation.Figure 2.16 Notation for Exercise 2.7.

3 Chapter 3Figure 3.1 Standard quadrilateral and triangular elements and .Figure 3.2 Trunk space. Illustration of spanning sets for , and .Figure 3.3 Product space. Illustration of spanning set for the space .Figure 3.4 Hierarchic shape functions for quadrilateral elements. Trunk spac...Figure 3.5 Isoparametric quadrilateral and triangular elements.Figure 3.6 Notation for (a) the standard triangular element and (b) quarter‐...Figure 3.7 Quadrilateral element with one curved side.Figure 3.8 Quadrilateral elements bounded by circular segments.Figure 3.9 The standard tetrahedral and pentahedral elements and .Figure 3.10 Meshing of a spherical surface with 202 triangular elements.Figure 3.11 Nodal forces associated with the 8‐node quadrilateral element. N...Figure 3.12 Example 3.3. Notation.Figure 3.13 Example 3.3. The smallest solution domain.

4 Chapter 4Figure 4.1 Reentrant corner. NotationFigure 4.2 The L‐shaped domain with a circular cut‐out. (a) Notation. (b) Th...Figure 4.3 The L‐shaped domain with a circular cut‐out ( ). Comparison of tw...Figure 4.4 The L‐shaped domain. (a) Notation, (b) radically graded 27‐elemen...Figure 4.5 The L‐shaped domain. Comparison of three discretization schemes. ...Figure 4.6 The L‐shaped domain with a circular cut‐out. (a) 18‐element mesh,...Figure 4.7 Definition of .Figure 4.8 Example 4.2: The first two normalized eigenfunctions.Figure 4.9 Multi‐material interface, notation.Figure 4.10 Example 4.3. (a) Notation. (b) Value of the determinant of the m...Figure 4.11 The Fichera domain, 189‐element mesh. (a) Uniform mesh: , , ....Figure 4.12 The Laplace problem on the Fichera domain. Comparison of three d...Figure 4.13 A problem of elasticity on an L‐shaped domain. Comparison of thr...Figure 4.14 (a) A typical compact tension test specimen. (b) A typical finit...Figure 4.15 One quarter of a compact tension test specimen. (a) Mesh detail,...Figure 4.16 (a) Loading by a concentrated force. (b) Loading by a step funct...Figure 4.17 Poisson ratio locking. Notation.Figure 4.18 (a) Rigid circular inclusion in an infinite plate under tension....Figure 4.19 Example 4.5. Rigid circular inclusion. The sum of normal stresse...Figure 4.20 Example 4.7. (a) Notation. (b) Isometric view and finite element...Figure 4.21 Example 4.7. Point convergence.Figure 4.22 Composite ring. Notation.Figure 4.23 Divergence of the maximum principal stress. The results were obt...

5 Chapter 5Figure 5.1 Rectangular beam in bending. Notation.Figure 5.2 The main elements of numerical simulation.Figure 5.3 Notation: (a) Truss element, (b) 3‐node plane stress or plane str...Figure 5.4 The main elements of finite element modeling.Figure 5.5 FEA timeline.Figure 5.6 The Girkmann problem. Notation.Figure 5.7 Lug problem. Notation.Figure 5.8 Surrogate problem. Notation.Figure 5.9 (a) Three‐dimensional contact problem. 50 pentahedral and 108 hex...Figure 5.10 Finite element mesh consisting of 2227 triangles. The constraine...Figure 5.11 Average displacement of the perimeter of the 25 mm diameter hole...Figure 5.12 Nodal forces. Notation.Figure 5.13 Coil spring.Figure 5.14 Solution domain and finite element mesh in the interval .Figure 5.15 Contours of the von Mises stress (MPa) on a 60 degree segment of...

6 Chapter 6Figure 6.1 Notch‐free test coupon. The dimensions are in inches. Thickness: ...Figure 6.2 The results of fatigue experiments performed on nine notched spec...Figure 6.3 Empirical relationship between the parameters a and r for 24S‐T3 ...Figure 6.4 Predicted and empirical cumulative distribution functions for the...Figure 6.5 Predicted and empirical cumulative distribution functions for the...Figure 6.6 The results of fatigue experiments performed on nine notched spec...Figure 6.7 Relationship between notch radius and notch sensitivity factor fo...Figure 6.8 The computed βk values and the function corresponding to Figure 6.9 24S‐T3 aluminum alloy: Combined qualified test records for the ni...Figure 6.10 (a) Specimen used in validation experiments. (b) Contours of von...Figure 6.11 Outcomes of axial, torsion and combined in‐phase fatigue experim...Figure 6.12 Survival function corresponding to ksi. Outcomes of combined i...Figure 6.13 Nominal stresses in experiments 1 and 2.Figure 6.14 Posterior pdf corresponding to three successes in three trials....Figure 6.15 Example 2: Prior and posterior pdfs.Figure 6.16 Ideal posterior pdfs corresponding to ideal data points, .Figure 6.17 Schematic representation of the validation process.

7 Chapter 7Figure 7.1 Notation.Figure 7.2 (a) Problem definition. (b) Bending moment diagram.Figure 7.3 The first four shape functions in one dimension.Figure 7.4 Problem definition for Exercise 7.8.Figure 7.5 Problem definition for Exercise 7.9.Figure 7.6 Sign convention for stress resultants.Figure 7.7 Transformation of stress resultants.Figure 7.8 Example 7.2: (a) Definition of the domain and 28 element mesh. Th...Figure 7.9 The rhombic plate problem, Exercise 7.17.Figure 7.10 Exercise 7.19. Equilateral triangle and rhombic plate. Notation...Figure 7.11 Infinite strip. Notation.Figure 7.12 Example 7.3. Contours of the third principal stress (MPa), pro...Figure 7.13 Example 7.5. The 20th eigenfunctions for (a) m and (b) m.Figure 7.14 Hyperboloidal shell.

8 Chapter 8Figure 8.1 RVEs for unidirectional laminae: (a) hexagonal and (b) rectangula...Figure 8.2 Solution domain consisting of 27 RVEs (864 finite elements).Figure 8.3 (a) Solution domain consisting of 8 RVEs (128 finite elements). (...Figure 8.4 Example. Equivalent strain in the matrix computed in the region o...

9 Chapter 9Figure 9.1 Notation.Figure 9.2 Elastic strip bent into a cylinder.Figure 9.3 The 20th modes of vibration of the elastic strip in Example 9.4. ...Figure 9.4 The first buckling modes of the cylindrical shell in Example 9.5....Figure 9.5 Typical uniaxial stress‐strain curve.Figure 9.6 Example 9.6. The force‐displacement relationship and the plastic ...Figure 9.7 Example 9.7: (a) The domain and the initial finite element mesh. ...Figure 9.8 Example: Contact problem in 1D. Notation.Figure 9.9 Example 9.9: Gap element with partial penetration.Figure 9.10 Axisymmetric model of two elastic spheres in frictionless contac...Figure 9.11 Contact pressure.

10 Appendix BFigure B.1 The error .

11 Appendix CFigure C.1 Fichera domain, elasticity. Convergence paths on uniform meshes....

12 Appendix DFigure D.1 The first eight shape functions based on Legendre polynomials.

13 Appendix FFigure F.1 The function yp on the optimal nodal set for .Figure F.2 Optimal interpolation points for the standard triangle, .

14 Appendix GFigure G.1 The function on the interval .

15 Appendix HFigure H.1 Notation.

16 Appendix IFigure I.1 Notched test specimens of type #3 and #6.Figure I.2 S‐N Data for 24S‐T3 (2024‐T3) aluminum alloy.Figure I.3 Bilinear S‐N curve for 24S‐T3 aluminum alloy.Figure I.4 MMPDS Fatigue limit model, S‐N curve for 24S‐T3 aluminum alloy.Figure I.5 Random fatigue limit model: S‐N data for 24S‐T3 aluminum alloy.Figure I.6 Empirical CDF of the S‐N data compared with the median predicted ...Figure I.7 Marginal cumulative distribution functions of the random fatigue ...Figure I.8 Profile likelihood and estimated confidence interval for μf ....

17 Appendix JFigure J.1 Notation.

18 Appendix KFigure K.1 Notation.Figure K.2 Coordinate transformation. Notation.Figure K.3 Statically equivalent forces and moments. Notation.Figure K.4 Example K.2: Segment of a coil spring.Figure K.5 Notation.