ملخص
Abstract
Behavior of constant thickness circular plates under axisymmetric uniform loading and for different edge boundary conditions may be obtained analytically, but for the case of variable thickness and transverse shear effect is usually difficult to follow analytically. Since the numerical analysis has become an essential tool in engineering mechanics, where the use of numerical methods enables the engineer to expand his or her ability to solve practical design problems, where the engineer may now treat real shapes as distinct from the somewhat limited variety of shapes amenable to simple analytic solution. That is why developing an appropriate numerical analysis becomes a more suited procedure to solve such problems. The standard stiffness procedure of finite element method may encounter some difficulty in formulation when dealing with both cases of variable thickness and transverse shear effect. The usually followed procedure is to utilize ring elements of constant thickness and increase the number of elements to reach an accurate solution. Mixed finite element formulation utilizing curved ring element with linearly varying thickness as well as considering the shear effect has proved to be successful to obtain accurate results for shells of revolution with small number of elements, due to the fact that the mixed formulation allows for nodal values in the form of global displacement components (ur, uz) and bending moment (Mr, M) as field variables, where second order polynomials may be used allowing for shear deformation effect to be considered as a function of moments and does not require higher order polynomials.