ASSUMED STRESS FUNCTION FINITE ELEMENT METHOD (STRUCTURES, COMPLEMENTARY ENERGY, BLENDING INTERPOLATION).
AdvisorGallagher, Richard H.
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PublisherThe University of Arizona.
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AbstractA finite element formulation, based on assumed stress functions, is developed for the linear elastic analysis of the stresses in two-dimensional elasticity problems, including multiply-connected regions and flat plate bending. For planar analysis the Airy stress function is utilized. The physical significance of the Airy stress function and its normal derivatives are brought out. A new technique is introduced to account for traction type boundary conditions. A family of rectangular finite elements, which enables the direct insertion of stress type boundary conditions, and two higher-order rectangular elements which enable continuous stress variations along the interelement boundaries are constructed using blending function interpolants. In addition, a C° continuous triangular plate bending element is adapted for use as a plate stretching element. The Southwell stress function is employed for the analysis of flat plates in bending. A computer program is developed to substantiate the proposed methodology. The formulations are evaluated through the comparison of solutions obtained from the proposed method with classical solutions and solutions obtained from the assumed displacement finite element method. The elements are evaluated by solving the same example problem with different element types. Extensions of the proposed method to account for body forces, initial stresses, material nonlinearities, and shells are briefly discussed. It is demonstrated that the proposed method can directly be integrated with minimal modifications into existing general purpose finite element programs.
Degree ProgramCivil Engineering and Engineering Mechanics