Study Of The Mechanic Performance Of Plates Nonlinearly Influenced By The Effect Of Initial Loads

With the development of structure design concept and the economy, under thepromise of guaranting the safety of structure, that much ligter, much stronger and muchthinner is the developing trendence of plate. However, that the plate mechanicalpreformance of plate,which is influenced by the effect of initial loads, is moreprominent. In the present paper, the effect of initial loads (including the effect of initialin-plane loads and the effect of initial transverse loads),which nonlinearly influencedthe static, dynamic and buckling performance of plates, are researched using the methodof combining theortical analysis and numeical simulation. The main innovationalcontents and conclusion are described as follows:①General form static and dynamic equilibrium differential equations consideredthe effect of initial transverse loads, and general form static and dynamic equilibriumdifferential equations considered the effect of both initial in-plane and transverse loadsare formulated. And corresponding polar coordinate form static and dynamicequilibrium differential equations, are also derived to fit the circular plate in axialsymmetrical conditions.②The finite element equation considered the effect of initial transverse loads, andfinite element equation considered considered the effect of both initial in-plane andtransverse loads are derived. The isoparameter plate element considered the effect ofinitial transverse loads, and both the rectangulr plate element and the isoparameter plateelement considered the effect of both initial in-plane and transverse loads are presentedfor arbitrary shape plates, and the corresponding programs are compiled by MATLAB.To better understand that static and dynamic performance of plates nonlinearlyinfluenced by the initial loads effects, numerical examples are discussed.③The approximate solutions of displacement and fundamental frequency, whichconsidered the effect of initial transverse loads, and the approximate solutions ofdisplacement and fundamental frequency, which considered the effect of both initialin-plane and transverse loads,`are derived for different shape plates. The approximatesolutions of first three frequencies considered the effect of initial transverse loads, andthe approximate solutions of first three frequencies considered the effect of both initialin-plane and transverse loads are solved for the simply supported rectangular plate.④The general form buckling differential equation and finite element equation considered the effect of initial transverse loads are formulated. The approximatesolutions of buckling critical load coefficient consiered the effect of initial transverseloads for three typical plates are solved. Numerical examples are conducted by thepresented FEM to better understand the effect of initial transverse loads on criticalbuckling loads of plates.⑤The effects of initial loads of plates, which influenced the static, dynamic andbuckling performance of the plate, are influenced by the initial loads, geometry,thickness plate, and the boundary condition of plate. In general, the plates with biggerinitial loads, smaller thickness, smaller stiffness and weaker boundary condition, themore obvious of the effects of initial loads on plates is.