Abstract
The stability problem of a rectangular plate supported at points of corners under uniform pressures in its median plane is studied by using the reciprocal theorem. At first, according to the differential equation of transversal buckling displacement function for a thin rectangular plate, dual trigonometric series, and the reciprocal theorem, the equation of the deflection surface for a rectangular plate with four simple supported edges under uniform pressures in its median plane and a transversal concentrated unit load is established. Secondly, using the reciprocal theorem, the buckling equation for a rectangular plate supported at points of corners is derived. The unknowns here can be determined by the boundary conditions. The exact solution of critical load is given. Finally, as an example, a square plate has been calculated. The results show that the method is accurate and effective to solve the stability problem of rectangular plates. It can serve as technical reference for engineering designs.
Highlights
Applications of thin elastic plate are broad in many fields of aerospace industry, civil engineering, and chemical engineering and so on
The reciprocal theorem is applied to research on the stability problem of a rectangular plate supported at points of corners under uniform pressures in its median plane
The results show that the method can solve the stability problem of rectangular plates with various boundary conditions
Summary
Applications of thin elastic plate are broad in many fields of aerospace industry, civil engineering, and chemical engineering and so on. Research methods about the stability problem of thin elastic rectangular plates are abundant [1-5]. There aren’t many studies of the exact solution for the stability problem of rectangular plates with complex boundary conditions. This is because the formulas of the stability problem are generally listed according to the boundary conditions at the stability analysis for the plate. The reciprocal theorem is applied to research on the stability problem of a rectangular plate supported at points of corners under uniform pressures in its median plane. The results show that the method can solve the stability problem of rectangular plates with various boundary conditions. It is effective to solve the stability problem of thin elastic plates
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