The influence of fiber volume content on the mechanical properties of two-dimensional (2D) plain carbon-fiber woven composites is a crucial concern that necessitates immediate attention for large-scale applications in wind turbine blades. In this study, various mechanical tests were conducted on 2D plain carbon-fiber woven composites with different fiber volume contents, and the influences of fiber volume content on the mechanical properties and failure mode of the composite material were analyzed. Using carbon fiber as reinforcement and epoxy resin as a matrix, three types of plates with fiber volume contents of 47%, 50% and 53% were fabricated by using autoclave technology. The tensile, compression and interlaminar shear tests of the two-dimensional woven composites were carried out using MTS series testing machines. The influences of fiber volume content on tensile strength and modulus, compressive strength and modulus, interlaminar shear strength and shear strain energy were investigated. Additionally, the progressive damage development of these two-dimensional woven composites under different stress states was studied using scanning electron microscopy (SEM). The results indicate that the tensile strength and compressive strength increase almost linearly with the increase in fiber volume content, while the interlaminar shear strength increases slowly at low fiber volume content and rapidly at high fiber volume content. The tensile modulus of elasticity slightly increases as the fiber volume content increases, whereas the compressive modulus remains stable at low fiber volume content but gradually decreases at high fiber volume content. With the increase in fiber volume content, the shear strain energy of the specimen increases significantly.

Cellular structure can possess superior mechanical properties and low density simultaneously. Additive manufacturing has experienced substantial progress in the past decades, which promotes the popularity of such bone-like structure. This paper proposes a methodology on the topological design of porous structure. For the typical technologies such as the p-norm aggregation and implicit porosity control, the violation of the maximum local volume constraint is inevitable. To this end, the primary optimization problem with bounds of local volume constraints is transformed into unconstrained programming by setting up a sequence of minimization sub-problems in terms of the augmented Lagrangian method. The approximation and algorithm using the concept of moving asymptotes is employed as the optimizer. Several numerical tests are provided to illustrate the effectiveness of the proposed approach in comparison with existing approaches. The effects of the global and local volume percentage, influence radius and mesh discretization on the final designs are investigated. In comparison to existing methods, the proposed method is capable of accurately limiting the upper bound of global and local volume fractions, which opens up new possibilities for additive manufacturing.

Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as freezing points, boiling points, melting points, infrared spectrum, electronic parameters, viscosity, and density of chemical graphs. We discuss these topological indices, and some of them are mentioned here such as Randic index, the first general Zagreb index, the general sum connectivity index, hyper-Zagreb index (HM), the atom-bond connectivity index (ABC), the geometric-arithmetic index (GA), the harmonic index (H), and the forgotten index (F).

Graph theory is a subdivision of discrete mathematics. In graph theory, a graph is made up of vertices connected through edges. Topological indices are numerical parameters or descriptors of graph. Topological index tells the symmetry of compound and helps us to compare those mathematical values, with boiling point, melting point, density, viscosity, hydrophobic surface area, polarity, etc., of that compound. In the present research paper, degree-based topological indices of Zeolite Socony Mobil-5 are calculated. Names of those topological indices are Randić index, first Zagreb index, general sum connectivity index, hyper-Zagreb index, geometric index, ABC index, etc.

This article proposes an augmented Lagrangian-based topology optimization approach to minimize the volume fraction subject to multiple nodal displacement constraints. The proposed method puts the multiple constraint equations in the objective function and transforms it into a sequence of unconstrained optimization problems. This study explains the theoretical aspects of the employed augmented Lagrangian approach in depth. Sensitivity expression in terms of design variables is identified by exercising the differentiate-then-discretize mechanism, and utilizes a moving asymptote algorithm to sort out a sequence of optimization subproblems. The optimized results are compared and analysed with those from conventional aggregation-based topology optimization. However, the predefined aggregation approach indicates a dependency on the supplied parameters. The numerical two- and three-dimensional examples reveal the viability and reliability of the suggested augmented Lagrangian scheme, which shows advantages in terms of robustness and efficiency.