Contents:Front Cover; Nonlinear Processes in Engineering; Copyright Page; Contents; Preface; Acknowledgments; Chapter 1. Invariant Imbedding; 1. Introduction; 2. An Elastic String; 3. Classical Imbedding; 4. Representation of the Solution; 5. An Analytical Example; 6. Variable Coefficients; 7. Numerical Aspects, Stability; 8. Invariant Imbedding; 9. Discussion; 10. Semigroup Properties; 11. Reciprocity Relation; 12. Computation of ui . A Two-Sweep Method; 13. A One-Sweep Method; 14. A Continuous Analog; 15. An Infinite String on Elastic Foundation; 16. Buckling. Classical Approach
17. Buckling. Invariant ImbeddingNOTES, COMMENTS, AND BIBLIOGRAPHY; Chapter 2. Differential Equations; I . Introduction; 2. Vector-Matrix Notation; 3. Systems of Ordinary Differential Equations; 4. Linear Homogeneous Systems. Superposition; 5. Linear lnhomogeneous System; 6. Variation of Parameters; 7. Constant Coefficients; 8. Higher-Order Equations; 9. Discussion; 10. Physical Systems. State Variables; 11. Initial-Value Systems; 12. Numerical Solutions; 13. Stability of the Numerical Process; 14. Two-Point-Value Problems; 15. Linear Two-Point-Value Problems
NOTES, COMMENTS, AND BIBLIOGRAPHYChapter 3. Beamlike Structures; 1. Introduction; 2. The Elementary Beam; 3. Higher-Dimensional Models Cylindrical Shells; 4. Semigroup Properties of Generalized Beams; 5. Invariant Imbedding. Perturbation Analysis; 6 . Matrix Riccati Transformations; 7. Validation of the Results; 8. Discussion; 9. A Two-Sweep Computational Method; 10. Invariant Imbedding. A One-Sweep Method; 11. Self-Adjoint Systems; 12. Numerical Stability; 13. General Two-Point Boundary Conditions; 14. Difference Equations; 15. Transfer Matrices; 16. The Scattering Matrix
17. The Flexibility MatrixNOTES, COMMENTS, AND BIBLIOGRAPHY; Chapter 4. Partial Differential Equations I; 1. Introduction; 2. Poisson's Equation; 3. Finite Elements; 4. Difference Equations; 5. Solution of the Equations; 6. Discussion; 7. Semidiscretization. The Elastic Plate; 8. A Stiffness Matrix; 9. Prescribed Displacements at Opposite Edges; 10. A Flexibility Matrix; 11. Numerical Example; 12. Buckling Problems. Critical Lengths; NOTES, COMMENTS, AND BIBLIOGRAPHY; Chupter 5. Partial Differential Equations II; 1. Introduction; 2. Formulation of the Problem; 3. Initial-Value Formulation
4. Reciprocity Relations5. Integral Riccati Transformations; 6. Computational Aspects; 7. Influence of Poisson's Ratio; 8. Invariant Imbedding Solution; NOTES, COMMENTS, AND BIBLIOGRAPHY; Chapter 6. Dynamic Programming; 1. Introduction; 2. A Linear String; 3. The Principle of Optimality; 4. An Analytical Solution; 5. Constraints; 6. A Nonlinear String; 7. A Routing Problem; 8. A Continuous Analog; 9. Euler Equations; 10. Convexity; 11. Numerical Aspects; 12. Discussion; 13. Partial Differential Equations; 14. The Biharmonic Equation; 15. Theorem of Castigliano; 16. Euler Equations
17. Natural Boundary Conditions