Finite Models and Methods of Dynamics in Structures

In view of the present level of computer techniques and the undoubted improvements in them which lie ahead, the finite methods of mechanics are and will remain the most universal tool for solving the dynamic problems of structures in civil and mechanical engineering and other applications. The aim of this volume is to create a unified system classifying the finite methods on the basis of their common features. A feature is found which is common to all known finite methods, and this feature is then formulated as a prerequisite for all known and unknown procedures. On the basis of this prerequisite, symptoms and factors of discretization are formulated; their combinations result in systems of factors denoting various finite models and the methods corresponding to them. Among the procedures obtained in this way are the existing methods and some new methods: some formulations of methods previously defined only in a stricter sense are also obtained. Various new and generalized existing methods are elaborated in practical applications. Some principles of mechanics are proposed for formulating the equations of motion of various finite models and they are applied to practical examples.

Table of Contents:
1. Introduction. Problems of discretization of a continuum. Division of the discretization problems into chapters. 2. Discretization of Continuum. Universal basis of finite methods. Process of discretization. 3. Symptoms and Factors of Discretization. Choice of symptoms of discretization. Division of the continuum into elements and location of centres. Distribution of deformation in the element. Arrangement of bonds. Bonds sensitive to displacements, velocities and accelerations. Factors of discretization. 4. Finite Models and Methods. Finite models. Finite methods. Displacement finite methods (DFM). Mesh discretization methods (MDM) and physical discretization methods (PDM). Finite element method (FEM). Rigid finite element method (RFEM). Physical finite element method (PFEM). Rigid physical finite element method (RPEM). Methods of classification: Degree IV; Degree V. Evaluation of the complete system of finite methods of mechanics. 5. Classification of the Existing Methods into a Complete System. Finite difference method. Ritz method. Rigid element chain method (RECM). Mass centres method (MCM). 6. Rigid Finite Element Method (RFEM). Formulation of the method. Application of REFEM to the dynamics and statics of structures. Application of RIFEM to the dynamics and statics of structures. 7. Rigid Physical Finite Element Method (RPFEM). Formulation of the method. Application of RPEFEM in the statics and dynamics of structures. 8. Functionals of Work and Energy and the Principles of Mechanics. Theory and fundamental relationships. Application of some laws and principles in: Indirect variational methods; Direct variational methods. Assessment and conclusion. 9. Methods of Solution of Systems of Differential and Algebraic Equations. Formulation of the problem and possibilities of mathematical operations. Transformation of the solution of a system of differential equations of motion into the solution of a simpler problem. Numerical methods for the solution of discrete equations of motion. Methods for solving the problem of eigenvalues. Methods of analysis of a static problem. 10. Numerical Calculations and their Assessment. Aims and methods of numerical calculations. Description of the system of the program. Examples and numerical results. Assessment of the results. 11. Assessment and Outline of Further Possibilities of Development. References. Index.