Optimization of layer composites with nontraditional interfaces for minimizing stresses Yasser M. Shabana, E. I. Imam Morgan Ahmed Elsawaf a Mechatronics Department, Faculty of Engineering and Materials Science, German University in Cairo New Cairo city, Egypt Yasser.shabana@gmail.com b Mechanical Design Department, Faculty of Engineering, Helwan University, El-Mataria, P.O.Box 11718 Cairo, Egypt Abstract—This article deals with an optimization problem of a thermal stress in a composite plate of three layers using the finite element analysis. The plate contains nontraditional interfaces as they have profiles following a power law. The interface profile parameter is optimized using the particle swarm optimization technique so that the maximum induced thermal stress in the structure is minimized. The optimum values of the interface profile parameter are evaluated at different temperatures and different heights of the nontraditional interface on the right surface relative to the mid-surface. Keywords—layer composites, nontraditional interfaces, particle swarm optimization technique, finite element analysis. I. INTRODUCTION Layer composite materials are playing important roles in different engineering applications. Therefore, many research works dealt with the behaviors of layer composites under different loading conditions. High stresses may induce at the interface between any two successive layers due to the properties mismatches. Different studies were accomplished to study the effect of the interferences on the induced stresses. Many researchers considered the interfaces as flat surfaces perpendicular to the lay-up direction of the layers [1-3]. On the other hand, nontraditional interface profiles were investigated concluding that the stresses can be reduced by the proper selection of the interference profile parameters [4]. Therefore, innumerable data are required for the best choice of the interface profile parameters. For more successful and efficient control of the stress, a further research is needed applying optimization methods. In this paper, the maximum induced stress in a three layer plate is minimized by optimizing the interface profile parameter. The finite element analysis is used to evaluate the thermal stresses in the plate. Whereas the particle swarm optimization technique [5], which is a nonlinear optimization technique, is used for optimizing the interface profile parameter. The optimum profile parameter of a nontraditional interface is evaluated for different applied temperatures and different heights of the nontraditional interface on the right surface relative to the mid-surface. II. PROBLEM STATEMENT AND SOLUTION Modifying the composite behaviors, such as the mechanical and thermal responses, is a main objective in order to be used for structures with severe loading conditions. These behaviors are depending mainly on the properties of the interfaces between the layers as they mostly exhibit the maximum weakness in a structure. The aim of the present study is to provide the designers of layer composites with better choices of the interface geometry so as to minimize the induced stresses and have safe designed components under different operating conditions. A three layer plate with both traditional and non-traditional interfaces, as shown in Fig. 1, is considered. While y-axis is chosen to be orthogonal to the faces of the layers and along their lay-up direction, x-axis is assumed to be orthogonal to the lay-up direction and parallel to the lamina faces. The origin of the coordinate system xy is supposed to lie at the midpoint of the lower face as shown in the figure. The top and bottom layers are made of alumina (Al 2 O 3 ) and nickel (Ni), respectively, while the intermediate layer made of a mixture of 60% Ni and 40 % Al 2 O 3 . Therefore, the ceramic volume fraction satisfies the following relations             1 2 1 1 2 1 c h y for 0 h h y h for 4 . 0 h h y for 1 v (1) For such cases, the through-thickness variation of the different properties, such as Young’s modulus, Poisson’s ratio and coefficient of thermal expansion, in the three-layer composite system can be written as             1 m 2 1 1 m c 2 1 c h y for P h h y h for ) P , P(P h h y for P P(y) (2) where P c and P m are the properties of the homogeneous ceramic and metal materials, respectively. P(P c , P m ) is the interlayer properties following the rule of mixtures. Also, the temperature-dependent properties [1] of the constituent materials are considered and these properties are assumed to vary linearly with the temperature. Therefore, the material