We numerically analyze three mechanics problems described below. For each problem, the developed computational model is verified by comparing computed results for example problems with those available in the literature. Effective utilization of single wall carbon nanotubes (SWCNTs) and single layer graphene sheets (SLGSs) as reinforcements in nanocomposites requires their strong binding with the surrounding matrix. An effective technique to enhance this binding is to functionalize SWCNTs and SLGSs by covalent attachment of appropriate chemical groups. However, this damages their pristine structures that may degrade their mechanical properties. Here, we delineate using molecular mechanics simulations effects of covalent functionalization on elastic moduli of these nanomaterials. It is found that Young's modulus and the shear modulus of an SWCNT (SLGS), respectively, decrease by about 34% (73%) and 43% (42%) when 20% (10%) of carbon atoms are functionalized for each of the four functional groups of different polarities studied. A shell theory that gives results close to the solution of the corresponding 3-dimensional problem depends upon the shell geometry, applied loads, and initial and boundary conditions. Here, by using a third order shear and normal deformable theory and the finite element method (FEM), we delineate for a doubly curved shell deformed statically with general tractions and subjected to different boundary conditions effects of geometric parameters on in-plane and transverse stretching and bending deformations. These results should help designers decide when to consider effects of these deformation modes for doubly curved shells. Composite laminates are usually fabricated by curing resin pre-impregnated fiber layers in an autoclave under prescribed temperature and pressure cycles. A challenge is to reduce residual stresses developed during this process and simultaneously minimize the cure cycle time. Here, we use the FEM and a genetic algorithm to find the optimal cycle parameters. It is found that in comparison to the manufacturer's recommended cycle, for a laminate with the span/thickness of 12.5, one optimal cycle reduces residual stresses by 47% and the total cure time from 5 to 4 hours, and another reduces the total cure time to 2 hours and residual stresses by 8%. / Ph. D. / We analyze using computational techniques three mechanics problems described below. In the last three decades, two carbon nanomaterials (i.e., allotropes of carbon having length-scale of 10^-9 m), namely, single wall carbon nanotubes (SWCNTs) and single layer graphene sheets (SLGSs) have evolved as revolutionary materials with exceptional properties per unit weight that are superior to conventional engineering materials. A composite (i.e., a material made by combining two or more materials to attain desired properties which cannot be achieved by any of its constituents alone) made by using either of these carbon nanomaterials as reinforcements in a polymer could be a potential candidate for applications requiring high strength and light weight. However, the effective utilization of these composites for an application requires the strong binding between their constituents. An effective technique to enhance this binding is to modify the surface properties of SWCNTs and SLGSs by covalently bonding to them suitable chemical group that is usually called covalent functionalization. However, this damages their pristine structures that may degrade their mechanical properties. Here, it is found that the functionalization reduces elastic moduli of carbon nanomaterials, the reduction increases with an increase in the amount of functionalization and is essentially independent of the functionalizing chemical group. This study should help engineers interested in utilizing these materials to design novel nanocomposites. Composite laminates, made by stacking and binding together layers of fiber-reinforced composites, are widely used in aircraft, aerospace, marine, automobile, power generation, chemical and ballistic applications due to their high strength and stiffness per unit weight compared to that of conventional metallic materials. Shell theories are widely used to analyze deformations of composite laminates which reduces a 3-dimensional (3-D) problem to an equivalent 2-D problem by making certain assumptions related to the deformations of the laminate. This approach requires less computational effort to find a numerical solution (i.e., an approximate solution obtained using a computational technique) of the problem as compared to that needed for solving the full 3-D problem. However, the accuracy of the results predicted by a shell theory depends on the problem being studied, i.e., the shell geometry, applied loads, initial conditions (i.e., the motion of the laminate at the start of application of the load) and boundary conditions (i.e., constraints imposed on the deformations of the edges of the laminate). Here, we analyze effects of geometric parameters of the laminated shells on their deformations for different types of applied loads and various boundary conditions specified on the edges. The results should help designers find an optimal geometry of the composite laminates for a given mechanical application. Fiber-reinforced composite laminates are usually fabricated by curing (which involves heating and cooling in a prescribed manner under application of the pressure) resin preimpregnated fiber layers under prescribed temperature and pressure cycles. However, during this cure process the laminate deforms and the final product is not stress-free. Here, we find optimal parameters of the cure cycle that minimize stresses developed during the cure process as well as the time required to cure the laminate. It is found that for a laminate studied these optimal parameters reduce the stresses by 47% and the cure time from 5 to 4 hours in comparison to the standard cure cycle recommended by the laminate manufacturer. This study will provide manufacturing engineers with an approach to fabricate composite laminates of desired quality.