Static Mechanical Properties Of Rectangular Thin Plates With Variation Thickness

Variable thickness plate is an important structural component in engineering practice.It is widely used in aerospace,civil engineering,vehicle engineering and many other fields.The mechanical properties of variable thickness plates are quite different from those of plates with uniform thickness.It is of great theoretical and practical significance to study the mechanical properties of variable thickness plates.In this thesis,the variable thickness plate is taken as the research subject,and the static deflection,internal force and critical buckling pressure of the variable thickness plate are calculated and analyzed.The details are as follows:1.Taking the variable thickness plate on uniformly distributed load as the research subject,the series and polynomials sum of the double sine function are taken as the deflection functions of the simply supported and clamped thin plate with variable thickness,respectively.The static deflection and internal force of the plate with equal thickness and variable thickness under the boundary conditions of simply supported on four sides and clamped on four sides are calculated by Galerkin method,and the Matlab program is compiled for numerical analysis.The numerical results show that the maximum static deflection of a plate with equal thickness is at the center of the sheet,while the maximum deflection of a plate with variable thickness is at the side of the plate with thin thickness.2.The static deflection of thin plates with the same size under the same boundary conditions and loading conditions is calculated by the difference method.The error analysis is carried out by comparing the results obtained by difference method with those by Galerkin method.3.Taking the thin variable thickness plates as the research subject.Applying longitudinal pressure on the plate in the change direction of thickness of the plate and in the orthogonal direction,respectively,the equation for solving the critical buckling pressure of variable thickness simply supported plate is established by the energy method.The numerical results show that when the aspect ratio of the plate is in certain intervals,plates with different thickness gradients have different buckling patterns and pressures.4.The critical buckling pressures of simply supported plates with different aspect ratios are calculated and analyzed.The critical pressure of the clamped variable thickness plate is obtained by the Galerkin method.The critical buckling pressures of clamped plates with different aspect ratios are calculated and analyzed.The numerical results show that the critical buckling pressures decreases with the increase of the plate thickness gradient.