BUCKLED PLATE VIBRATIONS, LARGE AMPLITUDE VIBRATIONS, AND NONLINEAR FLUTTER OF ELASTIC PLATES USING HIGH-ORDER TRIANGULAR FINITE ELEMENTS
Abstract
A high-order triangular membrane finite element is combined with a fully conforming triangular plate bending element to solve the geometrically nonlinear problems of plates where the membrane and flexural behavior are coupled and the effect of the inplane boundary conditions is as significant as the flexural boundary conditions. Each of the three orthogonal displacement components is represented by a two-dimensional polynomial of quintic order with no bias against one or the other giving the element a total of 54 degrees of freedom. The nonlinear stiffness matrices are formulated and an iterative procedure is used. Examples include the plane stress analyses of a parabolically loaded square plate, large deflections of a square plate under lateral pressure, postbuckling of a square plate, linear free vibration of a square plate with and without implane stresses. Various flexural and inplane boundary conditions are considered. Further the nonlinear finite element formulation is extended to analyze the supersonic nonlinear panel flutter problems. The quasi-steady aerodynamic theory is used. Limit cycle oscillation analyses are performed for two-dimensional and square panels. The effects of inplane compressive force, mass ratio, and inplane edge stress-free condition are considered. Stress distributions for the limit cycle oscillation of a two-dimensional panel are plotted. For the case of panels under static pressure differential, results for steady mean amplitude and flutter dynamic pressure are obtained for the two-dimensional and square panels, respectively. The effect of biaxial inplane compressive stress for a simply supported square panel is studied and boundaries separating the three regions namely the flat and stable region, dynamically stable buckled region, and the limit cycle oscillation region are found. Results are compared with those obtained by alternative finite element method, analytical approximate methods, and an experiment. Physical interpretations of the results and explanations of the discrepancies among various comparisons are given. The results indicate that the present development is capable of accurately solving a wide variety of geometrically nonlinear plate problems.
Degree
Ph.D.
Subject Area
Aerospace materials
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