International Journal of Computational Materials Science and Engineering

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers and analyzed its topological properties. For this purpose, we have computed topological indices, namely the Albertson index, the sigma index, the Nano-Zagreb index, the first and second hyper $F$-indices of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers.

Wavelets have generated significant interest from both theoretical and applied researchers over the last few decades. We proposed biorthogonal wavelet-based multigrid method for the numerical solution of elliptic partial differential equations. The performance of the proposed scheme is better than the existing ones in terms of superconvergence with low computational time. Some of the illustrative examples demonstrate the applicability of the method.

Thermal protection systems (TPS) are used in space applications to protect structures failing from burning and/or excessive temperatures. In this work, a finite element simulation is performed to analyze the behavior of a composite rocket motor casing during the expansion of combustion gases inside the motor. A two-dimensional axisymmetric model of a rocket motor casing provided with an insulating liner is modeled in a finite element software ANSYS. Variable equivalent heat flux at the inside faces of the liner, due to radiation and convection of gases, is estimated and applied as a boundary condition. The reduction of heat load with time due to latent heat of fusion and the resistance offered by char that exists above the pyrolysis front is also considered. At the same time, the material properties of the portion of the liner exposed to its melting point temperature are regulated to offer negligible resistance to move the boundary load on to the pyrolysis front at every instant. A transient analysis is carried out with appropriate mesh quality and time steps for 10 s. Ablation, charring, and unaffected regions are identified and the required insulation liner thickness is recommended. Extension of the procedure to model a similar motor with any other cylindrical length is discussed.

This study aims to explore the buckling behavior of rectangular plate with angle-ply overlay under thermal and mechanical loadings using meshless method. The governing differential equations (GDEs) of the plate are based on a new higher-order shear deformation theory (HSDT) and are discretized using polynomial radial basis function (RBF) to cast a set of equations simultaneously. A code is developed for the solution in MATLAB (2019). Uniform temperature differences and mechanical loads are the cause of in-plane loads. Convergence study has been conducted to check the current formulation’s soundness. The accuracy of the contemporary theory and formulation is validated with the published results. A parametric investigation is conducted for buckling behavior under the span-to-thickness ratio, lamination scheme, effect of the number of layers and effect of length-to-width ratio.

This work aims at analyzing the scaling behavior and develop correlations during surface growing for different germination lengths. The surface growing by random deposition is simulated using a kinetic Monte Carlo approach, by considering different germination lengths. Different surface descriptors are extracted, among them the roughness and the correlation. The former allows extracting the scaling behavior, while the latter proves the existence of correlations independent of the system size but dependent on the germination length. Moreover, as in the case of random deposition with a null germination length, the growing roughness never saturates.

Nowadays, osteoporosis disease that is related to aging has become a proliferating problem in worldwide society. It is therefore crucial to understand its evolution and predict this phenomenon precisely for different types of bone and volume fractions with adequate mathematical model. The application of statistical reconstruction method would be a helpful tool to predict osteoporosis for the simplified bone microstructures. To model osteoporosis evolution over time, in a first step, we propose to degrade the volume fraction with a mathematical model to reach any determined volume fraction between the initial condition and the degraded one with a statistical interpolation. In a second step, the degraded microstructure will be optimized using a statistical descriptor. The final optimized microstructures will be discussed as a function of the effective mechanical properties. The capability of quality of connection and two-point correlation functions (TPCFs) in 3D models and their application in the optimization of reconstructed interpolated models are going to be demonstrated. Finally, we will demonstrate and discuss the advantages of using the Quality of Connection Function (QCF) as a replacement of TPCF over the sole statistical descriptor named TPCF. We will show that QCF descriptor is better than TPCF only to find the optimized reconstructed models in a determined volume fraction.