The large deflection problem for a thin circular plate with different moduli in tension and compression has dually non-linear characteristics. In this paper, we use perturbation technique to obtain a general analytical solution of thin circular plate with different moduli in tension and compression, in which four edge conditions including rigidly clamped, clamped but free to slip, simply hinged and simply supported are considered. Because the perturbation solution is expanded in ascending powers of a known perturbation parameter (central deflection, for example) and the unknown constants and functions in the solution are gradually determined by decomposing boundary conditions and governing equation, the constants and functions obtained in such a manner have an inherent consistency concerning material properties. The results show that via construction of some parameters reflecting materials properties, not only the solution based on bimodular elasticity theory may regress to that on classical theory with singular modulus, but also the solution obtained under simply hinged edge may serve as a general solution to describe other three edge conditions. Via the general solution, the relations of load vs. central deflection, the plate–membrane transition for bimodular problem and the radial membrane stresses and bending stresses at the center and edge of the plate, are also discussed. Moreover, the comparison between the analytical solutions and numerical results indicates that the perturbation solutions based on the central deflection are overall valid. This work will be helpful for analyzing the mechanical behaviors of flexible layer structures while considering large deformation and bimodular effect.

General perturbation solution of large-deflection circular plate with different moduli in tension and compression under various edge conditions

Large-deflection axisymmetric deformation of circular clamped plates with different moduli in tension and compression

Materials which exhibit different elastic moduli in tension and compression are known as bimodular materials. The bimodular materials model, which is founded on the criterion of positive-negative signs of principal stress, is important for the structural analysis and design. However, due to the inherent complexity of the constitutive relation, it is difficult to obtain an analytical solution of a bimodular bending components except in particular simple problems. Based on the existent simplified model, this paper solves analytically bending thin plates with different moduli in tension and compression. By using the continuity conditions of stress components in unknown neutral layer, we determine the location of the neutral layer, and derive the governing differential equation for deflection, the flexural rigidity, and the internal forces in the thin plate. We also use a circular thin plate with bimodulus to illustrate the application of this solution derived in this paper. The results show that the introduction of different moduli has influences on the flexural stiffness of the bending thin plate.

An analytical solution of bending thin plates with different moduli in tension and compression

When materials that exhibit different mechanical behaviors in tension and compression must be analyzed, Ambartsumyan's bimodular model for isotropic materials can be adopted. It deals with the principal stress state in a point, which is particularly important in the analysis and design of structures. In this article, an equivalent section method is used to transform the bimodular curved beam into a classical one with singular modulus; consequently, the simplified solution for bending stresses may be easily determined only by changing a few parameters relating to section characteristics. For the determination of the unknown neutral layer, a perturbation method is used to obtain the explicit expression. Based on the known neutral layer, a stress function method is used to obtain the elasticity solution for stresses and displacements via boundary conditions and continuity conditions. Based on the elasticity solution, an initial stresses problem in a bimodular multiply-connected body is considered. The compar...

Analytical Solutions for Bending Curved Beams with Different Moduli in Tension and Compression

Many novel materials exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. Invest...

Nonlinear large deflection buckling analysis of compression rod with different moduli

When a different tension-compression elastic modulus is introduced into the statically indeterminate structure, the flexural rigidity EI is no longer a constant, which is different from that of classic mechanics, but becomes the function of the internal force, the calculation of the internal force in the structure is a nonlinear problem. In light of this, the formula of internal force in statically indeterminate structures with different moduli has been deduced, the iterative program for calculating nonlinear internal force developed, and examples analyzed. Finally, we put forth reasonable suggestions for calculating this kind of structure and a new idea in optimizing the structures by using different modulus characters. A new and simple analytical-iterative method has been provided for calculating practical engineering problems by using different-modulus theory. This is different from the previous complete numerical solution, which characterizes complex calculation procedure, heavy calculation work, and ...

Zhiming Ye

Papers

Internal Forces for Statically Indeterminate Structures Having Different Moduli in Tension and Compression