scholarly journals LOCALLY ORTHOTROPIC LAY-UP AS AN OPTIMAL SOLUTION FOR VAT POST-BUCKLED COMPOSITE PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE VON KARMAN LIMITS

2021 ◽  
Author(s):  
Sergey Selyugin
Keyword(s):  
Optimal Solution ◽  
Composite Plates ◽  
Maximization Problem ◽  
Large Deflections ◽  
Von Karman ◽  
Particular Solution ◽  
Principal Directions ◽  
The Moment ◽  
Curvature Tensors ◽  
Von Kármán

The present paper deals with the optimization of post-buckled VAT (variable angle tow) composite plates with large deflections. The Kirchhoff assumptions are used. The plates have a symmetric lay-up. The large deflection geometrically nonlinear theory above the von Karman limits is employed. The structural potential energy is treated as a measure of structural stiffness. For the plate stiffness maximization problem, the first-order necessary conditions of the local optimality are derived. The mathematical analysis of the conditions is performed. The conditions contain two terms. One of them corresponds to the mid-plane strains; another one corresponds to the generalized plate curvatures. A locally orthotropic lay-up is identified as an optimal solution. The local ply material direction is clearly coupled with the principal directions of 2D-strains and generalized curvatures. A particular solution of the linear combination of the ply optimality conditions is indicated. For the solution two pairs of the structural tensors are co-axial: the force and the strain tensors, as well as the moment and the generalized curvature tensors.

scholarly journals A KINEMATIC VARIATIONAL PRINCIPLE FOR THIN METALLIC AND COMPOSITE PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

2021 ◽  
Author(s):  
Sergey Selyugin
Keyword(s):  
Variational Principle ◽  
Plate Thickness ◽  
Composite Plates ◽  
Geometrically Nonlinear ◽  
Large Deflections ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Von Karman ◽  
Von Kármán ◽  
Thin Elastic Plates

Thin elastic plates (metallic or composite) experiencing large deflections are considered. The plate deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. The elongations, the shears and the in-plane rotations are assumed to be small. A kinematic variational principle leading to a boundary value problem for the plate is derived. It is shown that the principle gives proper equilibrium equations and boundary conditions. For moderate plate deflections the principle is transformed to the case of the von Karman plate.

scholarly journals THIN ELASTIC PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

2021 ◽  
Author(s):  
Sergey Selyugin
Keyword(s):  
Virtual Work ◽  
Plate Thickness ◽  
Geometrically Nonlinear ◽  
Large Deflections ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Virtual Work Principle ◽  
Von Karman ◽  
Von Kármán ◽  
Thin Elastic Plates

Thin elastic plates (homogeneous or composite) experiencing large deflections are considered. The deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. Small elongations and shears are assumed. Following Novozhilov, the strain expressions are derived. Then, under a small in-plane rotation assumption and using the virtual work principle, the equilibrium equations and the boundary conditions are obtained. The equations/conditions become the known von Karman ones for the case of moderate deflections. The solutions of the obtained equations may be used as benchmarks for the nonlinear structural analysis (e.g., FEM) software in the case of large deflections.

On Large Deflection of Symmetric Composite Plates under Static Loading

1986 ◽  
Vol 200 (1) ◽  
pp. 13-19 ◽  
Author(s):  
M Gorji
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Lateral Displacement ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Classical Plate Theory ◽  
Maximum Displacement ◽  
Von Karman ◽  
Non Linear ◽  
Von Kármán

The effect of transverse shear deformation on bending of elastic symmetric laminated composite plates undergoing large deformation (in the Von Karman sense) is considered in the present paper. The non-linear terms of the lateral displacement are considered as an additional set of lateral loads acting on the plate. The solution of a Von Karman type plate is therefore reduced to that of an equivalent plate with small displacements. This method offers an alternative technique for obtaining non-linear solutions to plate problems. The solutions of a number of example problems indicate that the non-linear shear deformation theory results, as expected, in higher values of the lateral displacement than the non-linear solutions from the classical plate theory. The difference in the values of the maximum displacement from both solutions, however, remains essentially constant beyond a certain value of the load. It is also noted that the linear and non-linear solutions deviate at a low value of w/h (w = maximum lateral displacement, h = thickness). Consequently, the extent of w/h within which the small deflection theory is applicable to composite plates is much lower than the value of 0.4 typically used for isotropic plates and depends, in general, upon lamination geometry and the degree of anisotropy.

A study of the behaviour of square plates at large deflections according to the theories of Foeppl and Von Karman

1978 ◽  
Vol 13 (1) ◽  
pp. 11-16 ◽  
Author(s):  
G J Turvey
Keyword(s):  
Variable Thickness ◽  
Large Deflections ◽  
Dynamic Relaxation ◽  
Asymptotic Nature ◽  
Von Karman ◽  
Von Kármán

Dynamic relaxation is used to analyse square plates at large deflections according to the Foeppl and Von Karman theories. The results quantify their asymptotic nature and the effect of variable thickness.

scholarly journals LAY-UP OPTIMALITY CONDITIONS FOR BUCKLING LEVEL MAXIMIZATION OF VAT (STEERED FIBER) COMPOSITE PLATES

2019 ◽  
Author(s):  
Sergey Selyugin
Keyword(s):  
Comparative Analysis ◽  
Optimality Conditions ◽  
Physical Meaning ◽  
Variational Principles ◽  
Fiber Composite ◽  
Composite Plates ◽  
Single Mode ◽  
Lamination Parameters ◽  
Von Karman ◽  
Von Kármán

IIn the present paper the flat composite plates in buckling are studied. The plates have a symmetric lay-up and loaded along their contour by the in-plane forces. The consideration employs the von Karman approach. The lay-up optimality conditions for a single-mode (lowest) buckling eigenvalue are derived using the proper variational principles and the variation calculus. Both the bending terms and the terms following from the redistribution of the 2D stresses over the plate are taken into account. The optimality conditions contain two items (corresponding to the bending and to the 2D infinitesimal plane strains). The comparative analysis of the items is performed. The physical meaning of the optimality conditions is demonstrated and explained. An illustration to the derived conditions is presented and analyzed. It is shown that for the optimal lay-up not all lamination parameters are independent on each other (one of them is a linearly dependent one). The analysis leads to a conclusion that the optimization w.r.t. the lamination parameters only is not sufficient for obtaining an optimal plate lay-up.

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