An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.

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A General Theory of Strength for Anisotropic Materials

Limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions. The general class of problems treated involves the geometric configuration of any number of isotropic or orthotropic layers bonded together and subjected to cylindrical bending. In general it is found that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios, but converges to the exact solution as this ratio increases. The analysis presented is also valid in the study of sandwich plates under cylindrical bending.

Exact solutions for composite laminates in cylindrical bending

Topology optimization of continuum structures: A review*

There are many technological applications for materials composed of short fibers interconnected by a bonding substance. In some naturally occurring cases, bone and teeth, the material is characterizable as oriented short fibers in a suitable matrix material. In the majority of cases, paper, leather, nonwoven fabrics and short fiber composites, the materials can be characterized as a random or nearly random arrangement of fibers in space. In this case the properties of an apparently homogeneous random or nearly random material can be treated as a laminated solid [1] [2]. In this approximation the homogeneous material is considered to be mathematically equivalent to a material composed of layers of oriented shortfiber material in which the percentage of fibers in each layer corresponds to the volume fraction of fibers of the particular orientation in the material being molded. Such a laminate for a random orientation of fibers is known as a &dquo;quasiisotropic&dquo; laminate [3] in laminated plate theory. Similar procedures [1] [2] [4] can be employed for the prediction of thermal expansion properties, transport properties, etc. The success of the lamination approximation is strongly dependent upon the assumption of physical volume averaging in real material systems combined with

Stiffness and Expansion Estimates for Oriented Short Fiber Composites

A novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested configurations. The applicability of the DMO method is demonstrated for fibre angle optimization of a cantilever beam and combined fibre angle and material selection optimization of a four-point beam bending problem and a doubly curved laminated shell. Copyright © 2005 John Wiley & Sons, Ltd.

Discrete material optimization of general composite shell structures

: Invariant properties of the elastic coefficient matrices of laminated composite plates are presented. The use of these invariants in materials evaluation and design optimization is discussed. Simple formulas, based upon micromechanics results, are derived for the invariants in terms of constituent material properties. (Author)

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N. J. Pagano

Papers

Invariant properties of composite materials.