Abstract
A way to approximate the compliance of composites for optimisation is described. A two-level approximation scheme is proposed inspired by traditional approximation concepts such as force approximations and convex linearisation. In level one, an approximation in terms of the reciprocal in-plane stiffness matrix is made. In level two, either the lamination parameters, or the nodal fibre angle distribution are used as design variables. A quadratic approximation is used to build the approximations in terms of the fibre angles. The method of conservative, convex separable approximations is used for the optimisation. Conservativeness is guaranteed by adding a convex damping function to the approximations. Two numerical examples, one optimisng the compliance of a plate clamped on the left, loaded downwards on the bottom right, another one optimising the compliance of a plate loaded with a shear force and a moment show the computational efficiency of the proposed optimisation algorithm.
Highlights
Composite materials are attractive due to their high stiffness-to-weight and strength-to-weight ratio
In the first step the optimal nodal stiffness distribution in terms of lamination parameters is found, in the second step the optimal fibre angles at the nodes are obtained, and in the third step the Responsible Editor: Jose Herskovits, Dr Ing
The material of the plate is assumed to be quasi-isotropic (QI), which is defined as all lamination parameters equal to zero
Summary
Composite materials are attractive due to their high stiffness-to-weight and strength-to-weight ratio. Fibres within a layer have the same orientation, leading to constant stiffness properties. As manufacturing technology has evolved, for example the advent of automated fibre placement machines, the fibre orientation of a layer can be varied continuously leading to varying stiffness properties that can be best tailored for the applied loads. These composites are called variable stiffness laminates (VSL). In the first step the optimal nodal stiffness distribution in terms of lamination parameters is found, in the second step the optimal fibre angles at the nodes are obtained, and in the third step the Responsible Editor: Jose Herskovits, Dr Ing
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