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Enriched Numerical Techniques : Implementation and Applications. (2024)

Jameel, Azher. ; Ul Harmain, Ghulam Ashraf. ; Singh, Indra Vir. ; [weitere]

San Diego :Elsevier Science & Technology,

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UID:

almahu_9949762855102882

Umfang: 1 online resource (481 pages)

Ausgabe: 1st ed.

ISBN: 0-443-15361-2

Anmerkung: Front Cover -- Enriched Numerical Techniques -- Copyright Page -- Contents -- List of contributors -- About the editors -- Preface -- 1 Development of level set methodologies for different geometric discontinuities -- 1.1 Introduction -- 1.2 Level set method -- 1.3 Normal level set function -- 1.4 Level set representation for closed discontinuities -- 1.5 Level set representation for cracks -- 1.6 Evaluation of split and tip elements -- 1.7 Effect of material irregularities on cracks -- 1.7.1 Displacement approximations -- 1.7.2 Evaluation of fracture parameters -- 1.8 Numerical results and discussions -- 1.8.1 Circular discontinuities -- 1.8.2 Elliptical discontinuity -- 1.8.3 Triangular discontinuity -- 1.8.4 Rectangular discontinuity -- 1.8.5 Hexagonal discontinuity -- 1.8.6 Octagonal discontinuity -- 1.8.7 A rectangular plate carrying cracks -- 1.8.8 Effect of size of inclusion -- 1.8.9 Effect of position of inclusion -- 1.8.10 Effect of size of hole -- 1.8.11 Effect of position of hole -- 1.9 Conclusion -- References -- 2 Higher order enrichment functions for fracture simulation in isotropic and orthotropic material medium -- 2.1 Introduction -- 2.2 Displacement approximation with extended finite element method -- 2.2.1 Partition of unity -- 2.2.2 Level set method with extended finite element method -- 2.2.3 Heaviside enrichment function -- 2.2.4 Branch enrichment functions for isotropic material -- 2.2.5 Branch enrichment functions for orthotropic material -- 2.2.6 Numerical integration -- 2.2.7 Fracture parameter (stress intensity factor) calculation -- 2.3 Result and discussions -- 2.3.1 Edge crack plate with an isotropic material medium -- 2.3.2 Center crack plate with isotropic material medium -- 2.3.3 Edge crack plate with an orthotropic material medium -- 2.3.4 Center crack plate with an orthotropic material medium. , 2.3.5 Edge crack with multiple holes orthotropic plate under fatigue loading -- 2.3.6 Edge crack with multiple holes/cracks orthotropic plate under fatigue loading -- 2.4 Conclusion -- References -- 3 Extended finite element method for three-dimensional cracks -- 3.1 Introduction -- 3.2 Extended finite element method for cracks -- 3.2.1 Choice of enrichment functions -- 3.3 Basic fracture mechanics principles -- 3.3.1 Linear elastic fracture mechanics principles -- 3.3.2 The stress intensity factor -- 3.3.3 The J-integral -- 3.3.4 The crack tip opening displacement -- 3.3.5 The interaction integral -- 3.4 Numerical results and discussions -- 3.4.1 Investigation of a plane edge crack -- 3.4.2 Cuboidal domain with a horizontal penny crack -- 3.4.3 Cuboidal domain with inclined penny crack -- 3.4.4 Cuboidal domain with a lens crack -- 3.5 Conclusion -- References -- 4 Extended finite element method for free vibration analyses of cracked plate based on higher order shear deformation theory -- 4.1 Introduction -- 4.2 Theoretical formulation -- 4.2.1 Partition of unity -- 4.2.2 Level set method -- 4.2.3 Enrichment -- 4.2.4 Selection of enriched nodes -- 4.2.5 Extended finite element approximation -- 4.2.6 Plate kinematics -- 4.2.6.1 Displacement field -- 4.2.6.2 Strain-displacement relation -- 4.2.6.3 Material constitutive relations -- 4.2.7 Modeling of functionally graded plate -- 4.2.8 Governing equation -- 4.2.8.1 Strain energy -- 4.2.8.2 Energy due to temperature rise and moisture rise -- 4.2.8.3 Kinetic energy -- 4.2.9 Numerical integration -- 4.2.10 Boundary conditions -- 4.3 Numerical results -- 4.3.1 Convergence and validation study -- 4.3.2 Parametric study -- 4.4 Summary -- References -- 5 Extended finite element method for stability analysis of stiffened trapezoidal composite panels -- 5.1 Introduction -- 5.2 Theory and formulation. , 5.3 The extended finite element method -- 5.4 Results and discussions -- 5.5 Conclusion -- References -- 6 Implementation issues in element-free Galerkin method -- 6.1 Introduction -- 6.2 Approximation function in element-free Galerkin method -- 6.3 Choice of weight (Kernel) function -- 6.3.1 Quartic spline weight function -- 6.3.2 Cubic spline weight function -- 6.3.3 Exponential spline weight function -- 6.4 Imposition of boundary conditions in element-free Galerkin method -- 6.4.1 Lagrangian multiplier method -- 6.4.2 Penalty method -- 6.5 Governing equations for element-free Galerkin method -- 6.6 Modeling of discontinuities in element-free Galerkin method -- 6.6.1 Methods based on modification of weight function -- 6.6.2 Methods based on modification of intrinsic basis -- 6.6.3 Methods based on extrinsic MLS enrichment -- 6.6.4 Methods based on extrinsic PUM enrichment -- 6.7 Level set method in element-free Galerkin method -- 6.8 h- and p-refinement -- 6.9 Numerical integration -- 6.9.1 Direct nodal integration -- 6.9.2 Stress point integration -- 6.9.3 Cell structure or background mesh -- 6.10 Conclusion -- References -- 7 Enriched element-free Galerkin method for three-dimensional cracks -- 7.1 Introduction -- 7.2 The element-free Galerkin method -- 7.2.1 Basic element-free Galerkin method models -- 7.2.2 Enriched element-free Galerkin method for cracks -- 7.2.3 Enrichment functions for cracks -- 7.3 Numerical results and discussions -- 7.3.1 Analysis of plane edge crack -- 7.3.2 Horizontal penny crack in a cubical domain -- 7.3.3 Inclined penny crack in a cubical domain -- 7.3.4 Lens crack in a cubical domain -- 7.4 Conclusion -- References -- 8 Enriched element-free Galerkin method for elastoplastic crack growth in steel alloys -- 8.1 Introduction -- 8.2 Governing formulations -- 8.3 Numerical formulation in elastoplastic analysis. , 8.3.1 Plasticity modeling -- 8.3.2 Analysis of elastoplastic stress-strain relations -- 8.3.3 Matrix representation of elastoplastic stress-strain relations -- 8.4 Stress calculation algorithms in elastoplasticity -- 8.4.1 Elastic predictor and plastic corrector algorithm -- 8.4.2 Implicit integration or von Mises plasticity -- 8.4.2.1 The radial return method -- 8.4.2.2 Material Jacobian for time-independent isotropic linear hardening plasticity -- 8.4.3 Plane stress plasticity -- 8.4.3.1 Plane stress-projected plasticity model -- 8.4.3.2 Plane stress-projected integration plasticity model -- 8.4.3.3 The plane stress-projected return mapping -- 8.4.3.4 The elastoplastic consistent tangent operator for plane stress plasticity -- 8.5 Investigation of fatigue crack growth -- 8.5.1 Computation of J-integral -- 8.5.2 Evaluation of fatigue life -- 8.6 Numerical results and discussions -- 8.7 Conclusion -- References -- 9 Enriched element-free Galerkin method for modeling large elasto-plastic deformations -- 9.1 Introduction -- 9.2 Large deformation theory -- 9.3 Introduction to element-free Galerkin method -- 9.3.1 Choice of weight function -- 9.3.2 Element-free Galerkin method models -- 9.4 Total Lagrangian formulation -- 9.5 Updated Lagrangian formulation -- 9.6 Large deformation in presence of discontinuities -- 9.7 Numerical results and discussions -- 9.7.1 Large deformation analysis with one bi-material surface -- 9.7.2 Large deformation analysis with two bi-material surfaces -- 9.7.3 Large deformation with a spherical interface -- 9.8 Conclusion -- References -- 10 Modeling of Hertzian contact problems by enriched element-free Galerkin method -- 10.1 Introduction -- 10.2 Hertzian classical theory -- 10.2.1 Contact between two spheres -- 10.2.2 Contact between an elastic half-space and a sphere -- 10.2.3 Two cylinders in contact with parallel axis. , 10.3 Continuum model of contact friction -- 10.4 Plasticity theory of friction -- 10.5 Governing equation for element-free Galerkin method -- 10.6 Lagrangian multiplier for contact problems -- 10.7 Imposition of contact constraints using penalty method -- 10.8 Analysis of the classical Hertzian contact problem: cylinder-rectangular block interaction -- 10.9 Conclusion -- References -- 11 Enriched element-free Galerkin method for large elasto-plastic deformations: basic mathematical foundations -- 11.1 Introduction -- 11.2 Kinematics of large deformation -- 11.2.1 The deformation gradient -- 11.2.2 Measures of stresses and strains -- 11.3 Large deformation analysis by element-free Galerkin method -- 11.3.1 Total Lagrangian formulation -- 11.3.2 Updated Lagrangian formulation -- 11.3.3 Large deformation in the presence of discontinuities -- 11.4 Elasto-plastic analysis -- 11.4.1 Elasto-plastic analysis in one dimension -- 11.4.2 Elastic-predictor plastic-corrector algorithm -- 11.4.3 General elasto-plastic analysis -- 11.4.3.1 The yield criteria -- 11.4.3.2 Strain hardening -- 11.4.3.3 Elasto-plastic stress-strain relations -- 11.4.3.4 Ramberg-Osgood model -- 11.5 Conclusion -- References -- 12 Implementation issues in extended isogeometric analysis -- 12.1 Introduction -- 12.2 Extended isogeometric analysis -- 12.2.1 Computer-aided design functions in extended isogeometric analysis -- 12.2.1.1 B-splines -- 12.2.1.2 Nonuniform rational B-spline -- 12.2.1.3 T-splines -- 12.2.1.4 Locally refined B-splines -- 12.2.1.5 PHT-splines -- 12.2.2 Fracture mechanics problem formulation -- 12.2.3 Approximation of voids and cracks using extended isogeometric analysis -- 12.2.3.1 Approximation of voids using extended isogeometric analysis -- 12.2.3.2 Approximation of cracks using extended isogeometric analysis -- 12.2.4 Selection of control points for enrichment. , 12.2.5 Extended isogeometric analysis-based discretization.

Weitere Ausg.: ISBN 0-443-15362-0

Sprache: Englisch

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