A New Finite Element Model for Stresses in Laminated Plates of Arbitrary Shapes

For safety reasons laminated glass are widely used in the world for many years, however it is one of the most complex composite that is rather difficult for analysis of displacements and stresses in its plates. The obvious reason is the placement of the elastomeric interlayer called polyvinyl butyral otherwise known as PVB. Even though this is a softer material compared to the stiffness of the glass plates, it provides some additional stiffness to the glass-PVB-glass composite which is beneficial to the user, but is very hard for the analysts. Early investigators relied on many experiments to come up with the stresses and displacements of laminated plates. For want of any mehtod of analysis, early researchers interested to compute the stresses and displacements, have resorted to a layered plate model neglecting the PVB in the composite. Later others developed a finite difference model for the complete analysis of the laminated glass. Recently some researchers have used three dimensional solid elements for the plates which is a possible approach but rather a tedious one. The finite difference model developed earlier was limited to rectangular plates, but engineers often use glass plates that are trapezoidal in shapes and sometimes with holes in them. These problems are very hard to be solved.

Here a new finite element model is developed. The element is a Mindlin plate element with 9 nodes and 5 degrees of freedom for each node. The methodology consists of a tangent element stiffness matrix with an incremental procedure to analyze the plate. The advantage of this element is that it can solve trapezoidal laminated glass or any other glass plate with different boundary conditions. Some example problems are solved and presented. The value of the stiffness of the PVB material can be changed nicely in this model. The model can be easily extended to analyze automobile wind shields.

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The Authors

Dr. C.V. Girija Vallabhan Texas Technical University Dr. Vallabhan received his Ph.D degree in Civil Engineering from the University of Texas, Austin, Texas in 1966. His speciality was application of finite element and finite difference methods to solve... Read more