The eigenbuckling analysis of hexagonal lattices: closed-form solutions

Elastic instability such as the buckling of cellular materials plays a pivotal role in their analysis and design. Despite extensive research, the quantifi- cation of critical stresses leading to elastic instabi- lities remains challenging due to the inherent nonlinearities. We develop an analytical approach considering the spectral decomposition of the elasticity matrix of two-dimensional hexagonal lattice materials. The necessary and sufficient condition for the buckling is established through the zeros of the eigenvalues of the elasticity matrix. Through the analytical solution of the eigenvalues, the conditions involving equivalent elastic properties of the lattice were directly connected to the mathematical requirement of buckling. The equivalent elastic properties are expressed in closed form using geometric properties of the lattice and trigonometric functions of a non-dimensional axial force parameter. The axial force parameter was identified for four different stress cases, namely, compressive stress in the longitudinal and transverse directions separately and together and torsional stress. By solving the resulting nonlinear equations, we derive exact analytical expressions of critical eigenbuckling stresses for these four cases. Crucial parameter combinations leading to minimum buckling stresses are derived analytically. The exact closed-form analytical expressions derived in the paper can be used for quick engineering design calculations and benchmarking related experimental and numerical studies.

Comparative analysis of the performance of mixing rules for density prediction of simple chemical mixtures

Four different mixing rules (MRs) in three equations of state (EOSs) have been used to account for the intermolecular forces of attraction between dissimilar molecules of different substances that form simple mixtures. The combined effects of the co-volumes of all constituent species of the mixtures were also considered, and the densities of these simple mixtures were predicted. Thereafter, the density results obtained were compared with accurately simulated experimental density values, and the effectiveness of these MRs was determined and compared. The four MRs compared are geometric mean average (GMA), whole square root average (SRA), Expanded geometric average (EGA), and simple average (SA) of attractive force parameter. They were all used in Van der Waals, Redlich Kwong, and Peng Robinson EOSs for two simple mixtures: a binary system (Ammonia – Water system) and a ternary mixture (methyl acetate – water – toluene system). It was found that GMA and EGA gave reasonably accurate estimates of the mixture attractive force parameter (am) and hence good density prediction for both Ammonia – Water and Methyl acetate – Water – Toluene systems. SRA gave unrealistic values of mixture densities for both systems and was discarded. SA gave a somewhat good result with Peng Robinson EOS for the ammonia-water system, but not that good in Redlich Kwong EOS and very poor in Van der Waals EOS. SA does not give reasonable estimates of the mixture densities with the three EOSs considered for the methyl acetate – water – toluene system.

Two methods for calculating the stress-strain state of shape memory alloy constructions taking into account tension-compression asymmetry

Two methods for calculating the phase-structural deformations of shape memory alloy (SMA) structures under complex stress conditions are considered. They both are based on the one-dimensional phenomenological model, which is built upon the relationship between the direct transformation and martensitic inelasticity diagrams, which makes it possible to uniformly describe strains in the phase and structural transformations, since both of the strain components are associated with the formation of oriented martensite. The ability of the model to describe a number of basic macromechanical effects caused by martensitic transformations in SMA was shown in our previous work. After the generalization to the case of a complex stress state it can successfully be used for solving certain engineering problems. The generalization of the model can be accomplished in two ways. The first method involves the construction of three-dimensional constitutive relations, proceeding from the previously developed one-dimensional relations and some simplifying hypotheses, and the numerical implementation of these relations by the finite element method. The second is the structural method, applicable to structures, in which the stress-strain state is described by one kinematic and one force parameter. This method suggests the use of structural diagrams of direct transformation and martensitic inelasticity, which are similar to the corresponding material diagrams, but establish the dependence of the phase-structural component of the kinematic parameter on the force parameter (not the dependence of phase-structural strains on the stress). Although the structural method is associated with the necessity to experimentally determine the structural diagrams, it has the advantage of significantly reducing the computational costs. Additionally, the article presents a comparison of two methods for describing the tension-compression asymmetry, and also develops a method taking finite deformations into account.

Parameter Estimation of Drag Coefficient and Rolling Resistance of Vehicles Based on GPS Speed Data

In this paper, a parameter estimation method of the model-based design approach is applied to estimate the drag coefficient and the rolling resistance coefficient of a vehicle. In fact, a constant-force parameter (c_const) and a velocity-square-force parameter (c_square) are in the vehicle model, and these result in the sum force applied along the translational DOF that models the vehicle. It is only an assumption that the constant force is the rolling resistance and the force proportional to the square of the velocity is the drag force of the air. Only GPS speed data is used for the estimation process. The conclusion is that parameter estimation is a good alternative when expensive measurement devices are not available to measure the force losses separately and directly.

Application of Genetic Algorithm for More Efficient Multi-Layer Thickness Optimization in Solar Cells

Thin-film solar cells are predominately designed similar to a stacked structure. Optimizing the layer thicknesses in this stack structure is crucial to extract the best efficiency of the solar cell. The commonplace method used in optimization simulations, such as for optimizing the optical spacer layers’ thicknesses, is the parameter sweep. Our simulation study shows that the implementation of a meta-heuristic method like the genetic algorithm results in a significantly faster and accurate search method when compared to the brute-force parameter sweep method in both single and multi-layer optimization. While other sweep methods can also outperform the brute-force method, they do not consistently exhibit 100% accuracy in the optimized results like our genetic algorithm. We have used a well-studied P3HT-based structure to test our algorithm. Our best-case scenario was observed to use 60.84% fewer simulations than the brute-force method.

Periodic mixed convection flow along the surface of a thermally and electrically conducting cone

The main aim of the present work is to highlight the significances of periodic mixed convection flow and heat transfer characteristics along the surface of magnetized cone by exerting magnetic field exact at the surface of the cone. The numerical simulations of coupled non-dimensional equations are computed in terms of velocity field, temperature and magnetic field concentration and then used to examine the periodic components of skin friction, ?w, heat transfer, qw, and current density, jw, for various governing parameters. A nice periodic behavior of heat transfer qw is concluded for each value of mixed convection parameter, ?, but maximum periodicity is sketched at ? = 50. It is also computed that the lower value of magnetic Prandtl number ? = 0.1 gets poor amplitude in current density but highest amplitude is sketched for higher ? = 0.5. The behavior of heat and fluid-flow in the pres?ence of aligned magnetic field is associated with the phase angle and amplitude of oscillation. It is also noted that due to the increase in magnetic force parameter, ?, there are wave like disturbances generate within the fluid layers. These disturbances are basically hydromagnetic waves which becomes more prominent as the strength of magnetic force parameter is increased.

Periodic mixed convection flow along the surface of a thermally and electrically conducting cone

The main aim of the present work is to highlight the significances of periodic mixed convection flow and heat transfer characteristics along the surface of magnetized cone by exerting magnetic field exact at the surface of the cone. The numerical simulations of coupled non-dimensional equations are computed in terms of velocity field, temperature and magnetic field concentration and then used to examine the periodic components of skin friction, ?w, heat transfer, qw, and current density, jw, for various governing parameters. A nice periodic behavior of heat transfer qw is concluded for each value of mixed convection parameter, ?, but maximum periodicity is sketched at ? = 50. It is also computed that the lower value of magnetic Prandtl number ? = 0.1 gets poor amplitude in current density but highest amplitude is sketched for higher ? = 0.5. The behavior of heat and fluid-flow in the pres?ence of aligned magnetic field is associated with the phase angle and amplitude of oscillation. It is also noted that due to the increase in magnetic force parameter, ?, there are wave like disturbances generate within the fluid layers. These disturbances are basically hydromagnetic waves which becomes more prominent as the strength of magnetic force parameter is increased.

Development and Validation of Nusselt Number Correlations for Mixed Convection in an Arc-Shape Cavity

The analytical study has been performed to investigate the combined effects of lid movement and buoyancy force parameter on mixed convective flow in an arc-shape cavity. The dimensional analysis based on Buckingham π-Theorem is used in the present study. It results in correlations for Nusselt number in terms of non dimensionalized parameters, viz. Re, Pr, Gr, θ etc. The correlations developed are validated against the experimental data of horizontal arc- shape cavity and numerical data of inclined arc-shape cavity obtained from open literature. The correlation developed in the present study for horizontal arcshape cavity is valid for wide ranges of Re varying from 30 to 1500 and Gr from 0 to 107. In inclined arc-shape cavity it is valid for Re varying from 30 to 1500, Gr from105 to 107 and inclination angle from 150to 600.The close agreement in the comparison between predicted results by correlation developed in the present study and reported Nu correlation shows the validity of the correlation.