Stability Of Orthotropic Plates Research Articles

Stability of orthotropic plates

The solution to the problem of the stability of a rectangular orthotropic plate is described by the numerical-analytical method of boundary elements. As is known, the basis of this method is the analytical construction of the fundamental system of solutions and Green’s functions for the differential equation (or their system) for the problem under consideration. To account for certain boundary conditions, or contact conditions between the individual elements of the system, a small system of linear algebraic equations is compiled, which is then solved numerically. It is shown that four combinations of the roots of the characteristic equation corresponding to the differential equation of the problem are possible, which leads to the need to determine sixty-four analytical expressions of fundamental functions. The matrix of fundamental functions, which is the basis of the transcendental stability equation, is very sparse, which significantly improves the stability of numerical operations and ensures high accuracy of the results. An analysis of the numerical results obtained by the author’s method shows very good convergence with the results of finite element analysis. For both variants of the boundary conditions, the discrepancy for the corresponding critical loads is almost the same, and increases slightly with increasing critical load. Moreover, this discrepancy does not exceed one percent. It is noted that under both variants of the boundary conditions, the critical loads calculated by the boundary element method are less than in the finite element calculations. The obtained transcendental stability equation allows to determine critical forces both by the static method and by the dynamic one. From this equation it is possible to obtain a spectrum of critical forces for a fixed number of half-waves in the direction of one of the coordinate axes. The proposed approach allows us to obtain a solution to the stability problem of an orthotropic plate under any homogeneous and inhomogeneous boundary conditions.

Stability of Orthotropic Plates on a Kerr Foundation

Stability of Orthotropic Plates on a Kerr Foundation

Factors influencing the elastic stability of orthotropic plates containing a rectangular cut-out

A parametric study of the elastic buckling loads for rectangular orthotropic plates with square or rectangular cut-outs has been carried out. The effect of cut-out size, cut-out location and orientation of principal material directions were all investigated, as well as the effects of changing the material modular ratio and shear modulus. Simply supported and fully fixed boundaries were both considered. The analyses employed the conjugate load-displacement method for elastic instability analysis applied to element discretization of the plates. The main conclusion from this work was confirmation that the presence of a hole could equally well raise the elastic critical load just as much as lower it, depending on the hole size, shape and location and also the aspect ratio of the plate. From the viewpoint of material properties, it was found that the shear modulus, an independent property for orthotropic materials, has a major influence on the critical load.

Stability of orthotropic plates on a Kerr foundation

Stability of orthotropic plates on a Kerr foundation

Method of constructing arproximate analytic relations for characteristics of the dynamic stability of orthotropic plates and shells under rapid loading

Method of constructing arproximate analytic relations for characteristics of the dynamic stability of orthotropic plates and shells under rapid loading

Stability of orthotropic plates slightly resistant to transverse strains

Stability of orthotropic plates slightly resistant to transverse strains

Buckling and Postbuckling of Orthotropic Plates

Theme T stability is considered of flat rectangular plates when in-plane biaxial loads are applied. The in-plane and bending elastic properties are orthotropic and the plate axes of symmetry and the elastic axes of symmetry coincide. Both the initial buckling and the reduction in stiffness occurring at the instant of buckling are considered. Numerous authors have considered the stability of orthotropic plates under biaxial load. Wittrick, * for example, has shown for the simply supported case among others that the parameters involved can be combined into one curve giving the buckling load for any plate. Reference 2 considers the buckling and postbuckling of a class of biaxially loaded laminated plates in the presence of bending-extensional elastic couplings. The present paper treats the stability of specially orthotropic plates with these couplings absent; a further rationalization is then possible, in which for any plate the proportional loss of stiffness at buckling can also be expressed in a single curve. For a particular plate, the combination of these universal curves, for buckling load and the loss of stiffness at buckling, allows unified consideration of the stability of simply supported biaxially loaded orthotropic plates. It follows that the relative stiffness at buckling (i.e., the ratio of plate stiffness immediately after buckling to that immediately before) depends on one parameter involving the elastic constants and the transverse load; this fact may be exploited in design.