The paper gives a set of basic relations characterizing the phenomena of viscous polymer resin flow through fiber reinforcement and the resin curing process. We describe the technological process of manufacturing composite structures. The influence of the resin curing process on values of residual stresses in composite constructions is analyzed taking into account two components: thermal shrinkage and chemical shrinkage of resins. For cases of 2-D structures, the method of formulating such tasks has been demonstrated. The types of design variables appearing in the optimization problems in this area are also presented. The 2-D optimization problems have been formulated. Various optimization problems are solved in order to demonstrate the influence of discussed relations on values of residual stresses and curing processes of thermosetting resins.

The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations.