Simulation Based Engineering in Solid Mechanics

Häftad, Engelska, 2018

AvJ.S. Rao,J. S. Rao

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Lagrangian solution was used to derive the governing differentialequations consistent with assumed deformation field and solution for deformations, strains and stresses were obtained.The finite element method most suitable for HPC is derived and the corresponding stiffness matrix for the element is derived.

Produktinformation

Utgivningsdatum2018-06-29
Mått155 x 235 x undefined mm
FormatHäftad
SpråkEngelska
Antal sidor200
FörlagSpringer International Publishing AG
ISBN9783319837819

Tillhör följande kategorier

Preface.- Introduction.- 1.1 Matrices.- 1.2 Vectors and Tensors.- 1.3 Energy Principle.- 2 Continuous Solid.- 2.1 External and Internal Tractions.- 2.2. Stress Definition.- 2.3. Equilibrium Relations.- 2.4. Strain.- 2.5. Stress -- Strain Relations.- 2.6 Strain Energy and Work.- 2.7 Von Mises Stress.- 3 Euler-Lagrange Equations.- 3.1 General Approach for solving Structural Problems.- 3.2 Other Applications of Euler-Lagrange Equation leading to Optimization.- 3.3 Derivation of Euler-Lagrange Equation through Delta Operator.- 4 Axially Loaded 1-D Structures.- 4.1 Simply Supported Bar.- 4.2 Simply Supported - Free Bar.- 4.3 Finite Element Method.- 4.4 Thermal Stresses.- 4.5 Principle of Virtual Work4.6 Minimization of Total Potential Energy.- 5 Twisting of a Rod.- 5.1 Finite Element Method for Torsion.- 5.2 Two Elements and Stiffness Matrix Assembly.- 5.3 Ritz Method for Torsion.- 6 Bending of a Beam.- 6.1 Bending by Energy Method.- 6.2 Beam with Axial Load (Beam-Column).- 6.3 Strength ofMaterials Approach.- 6.4 Beam Solution by Energy Method.- 6.5 Beam Finite Element.- 6.6 Buckling revisited.- 6.7 Galerkin Method for Tapered Beams.- 6.8 General Structures by Commercial Solvers.- 7. Epilogue.- Acknowledgements.- Index.