V.I. Shalashilin's Books

Problems of Nonlinear Deformation

The Continuation Method Applied to Nonlinear Problems in Solid Mechanics

By: E.I. Grigolyuk,V.I. Shalashilin

Write a review Read reviews Take a Quiz Solve Book Puzzle

Problems of Nonlinear Deformation

The Continuation Method Applied to Nonlinear Problems in Solid Mechanics

By: E.I. Grigolyuk,V.I. Shalashilin

Interest in nonlinear problems in mechanics has been revived and intensified by the capacity of digital computers. Consequently, a question offundamental importance is the development of solution procedures which can be applied to a large class of problems. Nonlinear problems with a parameter constitute one such class. An important aspect of these problems is, as a rule, a question of the variation of the solution when the parameter is varied. Hence, the method of continuing the solution with respect to a parameter is a natural and, to a certain degree, universal tool for analysis. This book includes details of practical problems and the results of applying this method to a certain class of nonlinear problems in the field of deformable solid mechanics. In the Introduction, two forms of the method are presented, namely continu ous continuation, based on the integration of a Cauchy problem with respect to a parameter using explicit schemes, and discrete continuation, implementing step wise processes with respect to a parameter with the iterative improvement of the solution at each step. Difficulties which arise in continuing the solution in the neighbourhood of singular points are discussed and the problem of choosing the continuation parameter is formulated.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

270

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401137765

ISBN 13

9789401137768

Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics

By: V.I. Shalashilin,E. B. Kuznetsov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics

By: V.I. Shalashilin,E. B. Kuznetsov

The optimal continuation parameter provides the best conditions in a linearized system of equations at any moment of the continuation process. This is one of the first books in which the best parametrization is regarded systematically for a wide class of problems. It is of interest to scientists, specialists, and postgraduate students of applied and numerical mathematics and mechanics.

Average ratings

N/A