Unconventional finite element method for nonlinear analysis of beams and plates

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Title: Unconventional finite element method for nonlinear analysis of beams and plates
Author: Kim, Wooram
Abstract: In this thesis , mixed finite element models of beams and plates bending are developed to include other variables (i .e . , the membrane forces and shear forces ) in addition to the bending moments and vertical deflection , and to see the effect of it on the nonlinear analysis . Models were developed based on the weighted residual method . The effect of inclusion of additional variables is compared with other mixed models to show the advantage of the one type of model over other models . For beam problems the Euler -Bernoulli beam theory and the Timoshenko beam theory are used . And for the plate problems the classical plate theory and the first -order shear deformation plate theory are used . Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions . In the linear convergence study , solutions are compared with analytical solutions available and solutions of existing models . For non -linear equation solving direct method and Newton -Raphson method are used to find non -liner solutions . Then , converged solutions are compared with available solutions of the displacement models . Noticeable improvement in accuracy of force -like variables (i .e . , shear resultant , membrane resultant and bending moments ) at the boundary of elements can be achieved by using present mixed models in both linear and nonlinear analysis . Post processed data of newly developed mixed models show better accuracy than existing displacement based and mixed models in both of vertical displacement and force -like variables . Also present beam and plate finite element models allow use of relatively lower level of interpolation function without causing severe locking problems .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -3003
Date: 2009-05-15

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Unconventional finite element method for nonlinear analysis of beams and plates. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -3003 .

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