On the Unsymmetrical Buckling of Orthotropic Annular Plates

Abstract eng:
The present work is devoted to the study of nonaxisymmetric buckling of orthotropic non-uniform plate under normal pressure. Large deformations of homogeneous circular plates under normal pressure produce compressive stresses at the edges, which may cause buckling of the axisymmetric equilibrium state ([1]). Classical shell theories do not permit to take into account specific structure features of soft biological tissue such as non-homogeneity and strong anisotropy. Therefore it was important to develop the analytical mathematical models based on refined 2D shell theories ([2]). The numerical models are also elaborated and analyzed by means of FEM software package. In present study nonaxisymmetric loss of stability of an orthotropic non-homogeneous plate, modeling the Lamina Cribrosa (LC) of a human eye was considered. LC, a porous connective tissue in the eye spanning the scleral canal, through which retinal ganglion cell axons pass as they exit the eye ([3]), was modeled as a orthotropic plate with radial and angular nonuniformity. It was also assumed that the modulus of elasticity in the transverse direction was much smaller than the modulus of elasticity in the plane of the plate. To study the effect of the decreasing rate of modulus of elasticity on the critical load and buckling mode (number of waves in circumferential direction) the calculations were performed for different rates of nonuniformity, but for constant average value of the in-plane elastic modulus. It was shown that the "initial imperfections of form" favour the buckling and decrease the buckling load. For a plate, which is transversely isotropic or/and nonuniform, it was shown that buckling of the nonaxisymmetric stress-strain state may occur even under a small load.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket