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The basic concepts of traditional mechanics of stressed structures are suitable for classical uniform structures made of homogeneous materials but not for complex structures such as a network plate or structures made of composite materials. In this book a new approach to stressed inhomogeneous structures is presented, leading to significant changes in the classical concepts of stressed bodies, especially plates, membranes, rods and beams. It is devoted to the mechanical design and optimization problems of composite structures, based on the asymptotic homogenization models and its modifications and on newly elaborated rigorous mathematical methods.§- Introduction into Homogenization Method as Applied to Stressed Composite Materials§- Stressed Composite Plates and Membranes§- Stressed Composite Rods, Beams and Strings.