Structural instabilities involving time dependent materials : theory and experiment

Citation

Minahen, Timothy M. (1992) Structural instabilities involving time dependent materials : theory and experiment. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7h70-2p51. https://resolver.caltech.edu/CaltechETD:etd-08082007-100442

Abstract

The creep buckling of viscoelastic structures is studied analytically and experimentally to investigate structural stability in the presence of time dependent materials. The theory of linear viscoelasticity is used to model polymeric column specimens subjected to constant compressive end loads. A strength of materials approach (Euler-Bernoulli beam theory) is employed to model the moment-curvature relation for the column. The growth of initial imperfections is calculated using the hereditary integral formulation. Solution techniques are developed for small displacements and then generalized to include the effects of large displacements and rotations. A failure criterion based on maximum deformation allows the column life to be estimated directly from the material relaxation modulus. A discussion generalizing the results to include plates and shells is presented.

Rectangular cross-section polymethylmethacrylate (PMMA) specimens with hinged boundary conditions are used to study viscoelastic buckling experimentally. Constant compressive end loads are applied using a servo-controlled load frame while the specimens are kept in a temperature cabinet at elevated temperatures (accelerating the creep behavior). Specimen shortening and out-of-plane deflections are monitored during the tests. The relaxation modulus of PMMA is approximated by a Prony-Dirichlet series and the model is used to simulate the laboratory experiments. Model and experimental results show good agreement during the "glassy" and slow growth phases of the column response. As the growth rate increases some deviations between theory and experiment are seen. It is shown that the deviations are not a result of geometric nonlinearities, but may, in part, be explained by material nonlinearities not accounted for in the model.

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