Computational Mechanics Research Trends.

Intro -- COMPUTATIONAL MECHANICS RESEARCH TRENDS -- COMPUTATIONAL MECHANICS RESEARCH TRENDS -- CONTENTS -- PREFACE -- Chapter 1 A NATURAL NEIGHBOUR METHOD BASED ON FRAEIJS DE VEUBEKE VARIATIONAL PRINCIPLE -- Abstract -- Introduction -- Virtual Work Principle -- Approximation of the Displacement Field -- Discretized Virtual Work Principle -- Linear Elastic Theory -- The Fraeijs de Veubeke Functional -- The Fraeijs de Veubeke Variational Principle -- Domain Decomposition and Discretization -- Equations Deduced from the Fraeijs de Veubeke Variational Principle -- Matrix Notation -- Numerical Integration -- Patch Tests -- Application to Pure Bending -- Application to a Square Membrane with a Circular Hole -- Extention to non Linear Materials -- Variational Equation ` -- Domain Decomposition and Discretization -- Matrix Notation -- Solution of the Matrix Equations -- Elasto-plastic Material with von Mises Linear Hardening -- Patch Tests -- Pure Bending of a Beam -- Square Membrane with a Circular Hole -- Extention to Linear Fracture Mechanics -- Introduction -- Domain Decomposition and Discretization -- Solution of the Equation System -- Patch Tests -- Translation Tests -- Mode 1 Tests -- Mode 2 Tests -- Bar with a Single Edge Crack -- Conclusions -- Annex 1: Construction of the Voronoi Cells -- Case of a Convex Domain -- Case of a non Convex Domain -- Annex.2: Laplace Interpolant -- Case of a Point X Inside the Domain -- Case of a Point X on the Domain Contour -- Annex 3. Particular Case of a Regular Grid of Nodes -- Laplace Interpolant -- Case 1: X between A and B -- Case 2: X between B and C -- Case 3: X between C and D -- Calculation of -- Annex 4. Introduction of the Hypotheses in the FdV Principle -- Calculation of1 -- Calculation of2 -- Calculation of3 -- Calculation of4 -- Calculation of5 -- Calculation of6 -- Calculation of 0.

Annex 5. Analytical Calculation of V and IH. -- Analytical Integration of V over a Triangle -- Analytical Integration of IH over a Triangle -- References -- Chapter 2 NUMERICAL AND THEORETICAL INVESTIGATIONS OF THE TENSILE FAILURE OF SHRUNK CEMENT-BASED COMPOSITES -- Abstract -- 1. Introduction -- 1.1. Characteristics of Shrunk Concrete -- 1.2. Algorithm to Produce a Shrunk Specimen -- 1.3. Lattice-Type Modeling of Concrete -- 1.4. Paper Structure -- 2. GB Lattice Model -- 3. Method to Simulate Mismatch Deformation Due to Matrix Uniform Shrinkage -- 4. Global Numerical Procedure -- 4.1. Mohr-Coulomb Criterion -- 4.2. Event-By-Event Algorithm -- 5. Theoretical Analyses of Influences of Pre-stressed Field -- 6. Numerical Examples and Discussions -- 6.1. Production of Shrunk Specimens -- 6.2. Tensile Examples on Specimens without the Shrinkage-Induced Stress: Case 1 and Case 2 -- 6.3. Analysis of a Typical Case for Shrunk Specimens: Case 3 -- 6.4. Influence of the Shrinkage Rate: Case 3-5 -- 7. Conclusions -- Acknowledgements -- References -- Chapter 3 RECENT ADVANCES IN THE STATIC ANALYSIS OF STIFFENED PLATES - APPLICATION TO CONCRETE OR TO COMPOSITE STEEL-CONCRETE STRUCTURES -- Abstract -- Introduction -- Statement of the Problem -- A. In the Plate (at the Traces of the Two Interface Lines J=1,2 of the I-Th Plate-Beam Interface) -- B. In Each (I-Th) Beam (iiiiOxyz System of Axes) -- For the Plate -- B. For Each (I-Th) Beam -- Numerical Solution -- A. For the Plate Transverse Deflection pw. -- B. For the Plate Inplane Displacement Components pu, pv. -- C. For the Beam Transverse Displacements ibw, ibv and for the Angle of Twist ibxθ. -- D. For the Axial Deformation ibu -- Numerical Examples -- Example 1 -- Example 2. -- Conclusion -- References.

Chapter 4 A SPRING-BASED FINITE ELEMENT MODEL FOR THE PREDICTION OF MECHANICAL PROPERTIES OF CARBON NANOTUBES AND THEIR COMPOSITES -- Abstract -- 1. Introduction -- 2. CNTs Nanostructure -- 3. Interatomic Interactions -- 4. Finite Element Formulation -- 4.1. Swcnt Modeling -- 4.2. MWCNT -- 4.3. Swcnt Reinforced Composite -- 4.3.1. Swcnt Reinforcement Modeling -- 4.3.2. Matrix Modeling -- 4.3.3. Interface Modeling -- 5. Numerical Results and Discussion -- 5.1. Static Behavior of SWCNTs -- 5.2. Static Behavior of Swcnt Reinforced Composites -- 5.3. Dynamic Behavior of SWCNTs -- 5.4. Dynamic Behavior of MWCNTs -- 6. Conclusion -- References -- Chapter5COMPUTATIONALMECHANICSOFMOLECULARSYSTEMS -- Abstract -- 1.Introduction -- 2.MolecularPhaseSpaceTrajectoryasaComplexDynamicalSystem -- 3.TheProblemofSymbolisation -- 4.HowComputationalMechanicsCanBeUsedtoFindaSuit-ableSymbolisation -- 4.1.TheDynamicsMakesthePartitionFiner -- 4.2.ComputationalMechanicsCoarsensthePartition -- 4.3.ThePartitionGeneratedbyComputationalMechanicsIstheMostIn-formativeOne -- 4.4.ThreeStagesofSymbolisation -- 5.Implementation -- 5.1.MolecularDynamicsSimulation -- 5.2.Symbolisation -- 5.3. -machineReconstruction:CSSR -- 5.4.SurrogateTimeSeries -- 6.Results -- 6.1. -MachineGrowswiththeLengthofTimeSeries -- 6.2.AnalysisoftheCausalStates -- 6.3.Non-stationaryModelofGrowing -Machine -- 7.Conclusions -- Acknowledgements -- References -- Chapter 6 MESHLESS APPROACH AND ITS APPLICATION IN ENGINEERING PROBLEMS -- Abstract -- 1. Introduction -- 2. Potential Problems -- 2.1. The Analog Equation Method -- 2.2. RBF Approximation for the Particular Solution pu -- 2.3. VBCM for the Homogeneous Solution -- 2.4. The Construction of Solution System -- Example 1: Nonlinear Poisson Problems -- 3. Steady-State Heat Conduction in Inhomogeneous Materials.

3.1. Governing Equation for Steady-State Heat Conduction in Isotropic Heterogeneous Media -- 3.2. Governing Equation for Steady-State Heat Conduction in Anisotropic Media -- 3.3. Implementation of the Meshless Method -- 3.4. The Virtual Boundary Collocation Method for the Homogeneous Solution -- 3.5. The Construction of Solving Equations -- 3.6. Numerical Assessment -- 4. Transient Heat Conduction in Functionally Graded Materials -- 4.1. Basic Formulas of Transient Heat Conduction -- 4.2. Meshless Formulation -- 4.3. The Backward Time Stepping Scheme -- 4.4. Numerical Assessment -- 5. Thermo-Mechanical Analysis of FGMs -- 5.1. Governing Equations for FGMs -- 5.2. Graded Types of FGM -- 5.3. RBF Approximation -- 5.4. Method of Fundamental Solutions -- 3.4. Final Complete Solutions -- 6. Thin Plate Bending -- 6.1.Basic Equations of Thin Plate Bending -- 6.2. Fundamental Solution And Determination of Source Points -- 6.3. Radial Basis Function (RBF) -- 3.4. Solution w(x) -- Appendix. First and Second Order Differentials of Fundamental Solutions and Approximated Particular Solutions -- A1. Fundamental Solutions and Their Derivatives -- A2. Approximated Particular Solutions and Their Derivatives -- A2.1. Power Spline (PS) Function -- A2.2. Thin Plate Spline (TPS) Function -- References -- Chapter 7 EXPLICIT DYNAMIC FINITE ELEMENT METHOD FOR FRACTURE OF SHELLS -- 1. Introduction -- 2. Representation of Fractured Shell Element -- 2.1. Shell Formulation with Fracture -- 2.2. Representation of Fractured Shell Elements -- 2.3. Computation of Element Kinematics -- 2.3.1. Belytschko Lin Tsay 4 Nodes Element -- 2.3.2. Discrete Kirchhoff Triangular Shell Element -- 3. Computation Procedures -- 3.1. Newmark Scheme -- 3.2. Computation of Lumped Mass Matrix for Cracked Elements -- 3.3. Computation of Element Internal Forces.

4. Material Model and Modeling of Fracture -- 4.1. Hardening Plasticity for Quasi-Brittle Material -- 4.2. Fracture Criterion -- 4.3. Cohesive Crack Model -- 5. Numerical Examples -- 5.1. The Simulations of a Thin Shell Cylinder under Hydrostatic and Impulsive External Pressure -- 5.2. Tearing of a Plate by Out-of-Plane Loading -- 6. Conclusion -- References -- Chapter 8 PROBABILISTIC INTERPRETATIONS OF THE TLM NUMERICAL METHOD -- Abstract -- Introduction -- Theory (Part I) -- The Fundamentals of TLM -- Lossless TLM Formulations in Two and Three Dimensions -- Lossy TLM Formulations in One Dimension -- Mesh Scaling -- Lossy TLM Formulations in Two and Three Dimensions -- Theory (Part II) -- Probabilistic Interpretations of TLM (The One-Dimensional Case) -- Probabilistic Interpretations in Two and Three Dimensions -- Problem with Existing Theory -- An Apparent Paradox in the TLM/Random Walk Equivalence -- Extension of Theory -- A Resolution to the Paradox of a Discrete Random Walker With Negative Probability -- A General Transition Probability for Walker Pairs -- Discrete Random Walks and Diffraction -- Application of Extended Theory -- A Particle Approach to Wave Diffraction Phenomena -- Conclusion -- Appendix I -- Generating Function Derivation of Eqn (1) in Main Text -- Two-Dimensional Expressions: Eqns (11), (12) -- Three-Dimensional Expressions: Eqns (13), (14) -- References -- Chapter 9 SOME OBSERVATIONS ON ACCELERATED NUMERICAL SCHEMES FOR THE LAPLACE EQUATION -- Abstract -- Introduction -- Theory I -- The Reverse Engineering of Numerical Schemes for the Laplace Equation -- I Jacobi Scheme -- II. Gauss-Seidel Scheme -- III. Successive Over-Relaxation -- IV. A Fraction of Error at (X) Over Two Previous Time-Steps Added to Gauss-Seidel Scheme -- V. A Fraction of the Error at (X) between N-th and (N+1)th Steps Added to Gauss-Seidel Scheme.

VI. A Fraction of the Error at (X) iver the Two Previous Steps Is Added to a Jacobi Scheme.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.