Symmetry, Bifurcation, and Computational Methods in Nonlinear Structural Mechanics (Buckling, Stability, Group)

Healey, Timothy James

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Description

Title

Symmetry, Bifurcation, and Computational Methods in Nonlinear Structural Mechanics (Buckling, Stability, Group)

Author(s)

Healey, Timothy James

Issue Date

1985

Department of Study

Civil Engineering

Discipline

Civil Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Applied Mechanics

Abstract

• The computation of global (equilibrium) solution branches of one-parameter systems arising in nonlinear structural mechanics is considered in this work. Particular emphasis is given to systems possessing spatial symmetry and to the exploitation of that symmetry in computational schemes.
• Strategies for accurately locating and classifying singular points, and methods for continuation through limit points and bifurcation points are presented. The techniques allow for branch switching at simple and multiple bifurcation points.
• The equilibrium equations of general nonlinearly elastic structures and solids possessing symmetry are shown to be covariant with respect to a specific set of linear transformations. These transformations form a group and are derived from the symmetry of the physical system. It is shown that the identification of covariance leads to a reduction in the original problem. Moreover, the group transformations can be used to generate new solution branches from known ones.
• The analysis of a lattice dome under uniform loading is presented. The structure possesses symmetry, which is exploited in the group-theoretic reduction procedure. Considerable computational advantage results on combining the continuation methods with the group-theoretic techniques. Several global solution branches were computed and are illustrated. The structure possesses an almost bewildering array of equilibrium states, and the solution set is rich in singular points. The computations include continuation through a variety of singular points, and branch switching at simple and multiple bifurcation points.

Graduation Semester

1985

Type of Resource

text

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