A series solution of the exact equation for thick orthotropic plates

By considering three-dimensional elasticity without any initial assumptions, the authors obtain the state equations for an orthotropic body. A series solution for a simply supported rectangular thick plate with arbitrary ratio between thickness and width under any given load is presented. Every fundamental equation of three-dimensional elasticity can be exactly satisfied and all the nine elastic constants can also be taken into account by the present method. Numerical results are obtained and compared with those of Reissner's and Ambartsumyan's theories and some references

An exact solution for the statics and dynamics of laminated thick plates with orthotropic layers

In this study, the three-dimensional state equation for the jth ply of a laminated thick orthotropic plate is established in the local coordinate system according to the knowledge which has been introduced in the paper by Sundara Raja Iyengar and Pandya (1983, Fiber Sci. Technol.18, 19–36). Because all the physical quantities appearing in the state equation are just the compatible quantities of the interfaces, it is extremly convenient to develop the state equation of the whole plate. Furthermore, the number of unknowns included in the final equations has no relationship with that of the plies of the plate. Exact solutions are presented for the statics and dynamics of a three-ply orthotropic thick plates with simply supported edges. Numerical results are obtained and compared with those of Srinivas and Rao (1970, Int. J. Solids Structures6, 1463–1481) and thin plate theory

Exact solutions of buckling for simply supported thick laminates

The three-dimensional state equations for the initial buckling of orthotropic thick plates are established in the Cartesian co-ordinate system in this paper without imposing any assumptions about the displacement models or stress distribution across the thickness of the cross-section. By using the continuity conditions of the displacement and stresses on each interface between any two adjacent layers, the state equations for the laminates, which consist of orthotropic layers, were obtained. A unified exact solution for the buckling of simply supported rectangular laminates with any given number of orthotropic layers is presented in the paper by means of the well-known Cayley-Hamilton theorem. All the equations of elasticity can be satisfied exactly and the nine elasticity constants of orthotropy for each layer are fully taken into account. Regardless of the number of the layers considered, only a set of simultaneous linear algebraic equations of 3rd order needs to be solved in the final stage of the solution. The numerical results were calculated and compared with those of thin plate theory, Mindlin analysis and those due to Srinivas et al. who also solved the problems with the three-dimensional theory of elasticity

Exact Solutions for Axisymmetric Vibration of Laminated Circular Plates

Based on fundamental equations of three‐dimensional elasticity and giving up any assumptions about displacement models and stress distribution, the state equations for the axisymmetric free vibrations of transversely isotropic circular plates are established. Because the four quantities appearing in the state equations happen to be the compatibility quantities of the interfaces, it is extremely convenient to develop the state equations of laminated circular plates with transversely isotropic layers. The exact solutions for such problems with simply supported and clamped edges are presented in this paper. Every fundamental equation of three‐dimensional elasticity can be exactly satisfied and all five elastic‐flexibility constants can also be taken into account by the present method. No matter how many layers are considered, the calculation always leads to solving a set of linear algebraic equations of the second order. Numerical results are obtained and compared with the results calculated using the Reissner and Mindlin theories, respectively