Nonlinear dynamic analysis of cable and membrane structures Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/x920g0650

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  • The nonlinear dynamic analysis of cable and membrane structures is presented in this study. Attention is given to the nonlinearities arising from large displacements, from nonlinear stress-strain relationships and from nonconservative loadings. The finite element method is used to model the cables and membranes. Curvilinear geometries of the elements are approximated by using higher-order interpolation polynomials. The relative advantages and disadvantages of adopting elements with various orders of approximating functions are determined by a variety of example problems. Full interaction between the cables and membranes in a structure can be realized by selecting compatible elements. Any desired nonlinear constitutive equation can be specified for the cable and membrane elements. The ability to handle nonconservative loadings is demonstrated by studying the dynamic responses of cables and membranes in a fluid medium. The governing equations of motion of cables and membranes are derived from the three-dimensional equations of finite elasticity. Curvilinear, convected coordinates are used to describe the undeformed and deformed configurations of a body. The total Lagrangian description and the principle of virtual work are used to formulate the equilibrium equations. Specializations to cables and membranes are made by assuming that states of uniaxial stress and plane stress exist in the cables and membranes, respectively. The magnitudes of the displacements and strains are not restricted. Explicit stressstrain relationships are neither assumed nor required. Isoparametric representation is used to formulate curved cable and membrane finite elements. The element matrices are evaluated by numerical integrations. The global dynamic equations of motions are integrated by the Newmark's method. An iteration scheme is used to minimize the residual errors. Numerical examples are included to demonstrate the validity and capability of the finite element models and the solution techniques. Higher-order elements are found to be more accurate than linear elements in general, but are computationally more costly. The potential of the finite element method in analyzing the nonlinear dynamic response of submerged cable and membrane structures to wave forces is demonstrated.
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