Vibration and buckling of laminated plates of complex form under in-plane uniform and non-uniform loading (Q2067033)

The vibration and buckling analysis of symmetrically laminated plates with complex form subjected to in-plane uniform and non-uniform loading is performed using variational Ritz's method and the R-functions theory. First-order shear deformation theory of Timoshenko's type is adopted. Each ply is assumed to be an orthotropic homogeneous one without slip at interfaces. The developed approach includes several stages: determination of the heterogeneous subcritical state of the plate; finding buckling critical load; solving linear vibration problem. Ritz's method is applied on each stage. Systems of the admissible functions, that satisfy at least main (kinematic) boundary conditions have been built by the R-functions method. Validation of the proposed method and created software is confirmed by comparison of buckling load and vibration frequency with known results for square laminated plates of free circular or rectangular cut-outs. Buckling loads for laminated clamped plates with complex form under non-uniform edge compressions have been obtained. It is assumed that plates can be made of different materials and have different ply orientations. The effects of the cut-out sizes on critical load and frequency are studied together with the effects of number of layers, degree of orthotropic boundary conditions and type of loading (uniform and non-uniform). There exists many situations when subcritical state of a plate may be inhomogeneous: a plate has cut-out or complex form; external load acting along boundary is non-uniform, and other cases also. The proposed method allows to solve a wide class of similar problems, including plates with cut-outs. Some results obtained by the proposed method are presented. For the entire collection see [Zbl 1477.93111].