Nonlinear Finite Elements for Continua and Structures - Info and Reading Options

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Intro -- Nonlinear Finite Elements for Continua and Structures Second Edition -- Copyright -- Contents -- Foreword -- Preface -- List of Boxes -- 1 Introduction -- 1.1 Nonlinear Finite Elements in Design -- 1.2 Related Books and a Brief History of Nonlinear Finite Elements -- 1.3 Notation -- 1.3.1 Indicial Notation -- 1.3.2 Tensor Notation -- 1.3.3 Functions -- 1.3.4 Matrix Notation -- 1.4 Mesh Descriptions -- 1.5 Classification of Partial Differential Equations -- 1.6 Exercises -- 2 Lagrangian and Eulerian Finite Elements in One Dimension -- 2.1 Introduction -- 2.2 Governing Equations for Total Lagrangian Formulation -- 2.2.1 Nomenclature -- 2.2.2 Motion and Strain Measure -- 2.2.3 Stress Measure -- 2.2.4 Governing Equations -- 2.2.5 Momentum Equation in Terms of Displacements -- 2.2.6 Continuity of Functions -- 2.2.7 Fundamental Theorem of Calculus -- 2.3 Weak Form for Total Lagrangian Formulation -- 2.3.1 Strong Form to Weak Form -- 2.3.2 Weak Form to Strong Form -- 2.3.3 Physical Names of Virtual Work Terms -- 2.3.4 Principle of Virtual Work -- 2.4 Finite Element Discretization in Total Lagrangian Formulation -- 2.4.1 Finite Element Approximations -- 2.4.2 Nodal Forces -- 2.4.3 Semidiscrete Equations -- 2.4.4 Initial Conditions -- 2.4.5 Least-Square Fit to Initial Conditions -- 2.4.6 Diagonal Mass Matrix -- 2.5 Element and Global Matrices -- 2.6 Governing Equations for Updated Lagrangian Formulation -- 2.6.1 Boundary and Interior Continuity Conditions -- 2.6.2 Initial Conditions -- 2.7 Weak Form for Updated Lagrangian Formulation -- 2.8 Element Equations for Updated Lagrangian Formulation -- 2.8.1 Finite Element Approximation -- 2.8.2 Element Coordinates -- 2.8.3 Internal and External Nodal Forces -- 2.8.4 Mass Matrix -- 2.8.5 Equivalence of Updated and Total Lagrangian Formulations

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