finite element method

In this article, the analysis of free and forced vibrations of a microplate based on the Kirchhoff gradient strain theory with clamped boundary conditions is presented using the finite element formulation with  continuity. Due to the presence of higher-order derivatives,  continuous interpolation functions are employed to provide a standard formulation. Subsequently, the stiffness and mass matrices of the microplate element are extracted using the Hamiltonian principle, and the formulation is applied to a four-noded quadrilateral element with 36 degrees of freedom. The natural frequencies of the desired microplate are obtained using the finite element method and compared with analytical results. Additionally, by refining the element dimensions (mesh refinement), the accuracy of this method is compared by examining the obtained frequencies with the finite element method and the desired analytical results. Furthermore, the natural frequencies for microplates with different boundary conditions are provided, and the influence of the  ratio on the natural frequencies of microplates with various boundary conditions is investigated.Subsequently, vibration diagrams for the microplate with specified initial conditions and applied forces are presented. The effects of boundary conditions and the  ratio on various microplate parameters are examined and discussed.

Unlike triangular/tetrahedral elements used in the finite element method for two/three-dimensional problems, local refinement of meshes composed of quadrilateral/hexahedral elements while maintaining the compatibility is challenging, and often results in severe distortion of the elements. A well-known and widely used approach to address this issue is the local mesh refinement based on transitional elements with hanging nodes. The key point in this method is enforcing the displacement continuity at the transitional element boundaries in the presence of hanging nodes. Transitional elements introduced in the literature employ various formulations depending on their placement within the mesh, and are also constrained by a maximum number of hanging nodes. along the element boundary. Therefore, their implementation for a general case is quite complicated. This paper presents a novel transitional element based on alternative shape functions, which offers a unified formulation for different placements of transitional elements in the mesh, applicable to any number of hanging nodes. Additionally, an analytical proof is provided to demonstrate the continuity and partition of unity properties in the proposed method, used in local mesh refinement. Finally, numerical examples in two and three dimensions are simulated to compare the accuracy and convergence of the proposed method against the existing methods in the literature.

The present study investigates the cooling of a heated rectangular plate through fluid flow in a channel, utilizing the interaction between solid and fluid with two elastic walls under oscillating conditions and external forces. The incompressible fluid flow passes through a two-dimensional channel containing a constant heat flux heat source in the center, with two identical and equally sized elastic walls positioned at the top and bottom of the channel. As the fluid flows over the heated surface and the elastic walls oscillate, the rate of heat transfer to the fluid changes. In this scenario, the heat exchange rate behaves as a function of the conditions of the oscillating elastic surfaces, the magnitude of the force applied to the elastic walls, and the oscillation period of the applied force. The goal of the simulations conducted is to examine the application of replacing the elastic boundary with a rigid boundary in part of the channel and the impact of oscillation period and force magnitude. In this study, laminar flow with four different Reynolds numbers (600, 1100, 1600, and 2100) and three different applied force amplitudes (200, 400, and 800 N/m) alongside four oscillation periods (0.5, 0.25, 0.125, and 0.07 seconds) has been analyzed After solving the governing equations, including the energy equation, momentum equations, and elastic surface equations, utilizing the arbitrary Eulerian-Lagrangian method in COMSOL engineering software, the results indicate that decreasing the oscillation period enhances fluid flow mixing, thereby increasing the heat transfer rate to its optimal level. The findings show that a continuous reduction of the applied force’s oscillation period to an optimal level can be effective; conversely, exceeding this optimal point can negatively impact the heat dissipation rate. The highest percentage increase in the convective heat transfer coefficient, compared to the rigid channel, at a constant applied force of 800 N/m for Reynolds numbers 600, 1100, 1600, and 2100 were 301%, 297%, 341%, and 328%, respectively. 

The human body is exposed to many forces and torques during daily activities. The spine is one of the most important organs that bears these forces and may be prone to multiple injuries. Therefore, numerical modeling and analysis of the lumbar spine under various loading conditions is very beneficial to prevent injuries. This study aims to provide a valid finite element model of the L4-L5 segment of the human lumbar spine for static analysis. The model includes two vertebrae, intervertebral discs, end plates, and ligaments. To model the mechanical properties of the lumbar spine, elastic and hyperelastic behaviors have been used for different parts of the spine. Moreover, stress and strain distribution in different tissues, under various loading conditions, were compared with the allowable thresholds of the tissues to investigate the possibility of the tissue damage. Note that it was assumed that the tissue damage occurs when the stresses and strains in the desired tissue exceed the elastic range. However, based on the obtained results, under the investigated loading conditions, none of the model components were damaged.

This research focuses on topology optimization of fluid-structure interaction (FSI) problems using the level set method. To couple the fluid and structure equations, the Arbitrary Lagrangian-Eulerian (ALE) description is employed within a monolithic formulation. The use of ALE in FSI problems, while eliminating numerical instabilities caused by the convective term, enhances the speed and accuracy of finite element solutions in fluid-structure interaction. Additionally, considering the fluid in the unsteady state allows for the interpretation of optimal topology at any given moment of the analysis. The objective function of the optimal topology design problem is to minimize the structural compliance in the dry state, subject to a fixed volume of the design domain. To determine the normal velocity in the reaction-diffusion equation (RDE), adjoint sensitivity analysis based on pointwise gradients is used. The results obtained from this approach, compared to other topology optimization methods in the literature, demonstrate higher accuracy and clearer definition of structural boundaries.

In this study, the vibrations of a folded plate made of auxetic cells were examined. Initially, the elastic constants and density of the auxetic plate were determined based on the geometrical and material parameters of unit cell. The folded plate was considered as two jointed rectangular plates. Utilizing the first-order shear deformation theory and applying Hamilton's principle, the equations of motion governing each plate and the boundary conditions at the plate's edges were derived. Next, employing the combined Levy-differential quadrature method, the transformed equations of motion from the partial type to ordinary one has been solved. Assembling the equations of motion with boundary and continuity relations leads to an eigenvalue problem that its solution can present the frequency response function of folded plate. To validate the results obtained from the Levy-differential quadrature solution, the auxetic plate was simulated by a finite element analysis software (ABAQUS), and the comparison results demonstrated the accuracy of presented analytical method. Finally, the effects of plate's geometrical parameters on the natural frequencies of the folded plate were investigated. The results showed that by changing the folding angle from 180 degrees to less, or in other words, by converting the flat plate to a folded plate, the natural frequency first increases and then remains almost constant.

Cardiovascular diseases are the leading cause of death worldwide. Computer simulations of cardiac function are gradually becoming a powerful tool to better understand cardiac behavior and support clinical decision-making. However, right heart modeling is still in its early stages. Pulmonary hypertension is a pathophysiological disorder that may involve several clinical conditions. This study presents a fully coupled multiscale mathematical and numerical model of cardiac electromechanics with idealized biventricular geometry for normal subjects and pulmonary hypertension patients in COMSOL software. Muscle fibers that control electrical conduction and myocardial contraction, is one of the vital factors for the electromechanical simulation of the heart which was defined using a rule-based method. Windkessel blood circulation model was used to calculate systemic and pulmonary pressures. Blood circulation was modeled with a straightforward approach for the left and right ventricles. Lastly, alterations in the functional behavior of the heart were evaluated between individuals without pulmonary hypertension and healthy subjects. It was observed that right ventricular pressure increases in pulmonary arterial hypertension and ejection fraction decreases.

In this study, the layerwise theory, along with the first-order shear deformation theory, was employed to investigate the relaxation of stresses in the adhesive layers of a symmetric five-layer square sandwich plate subjected to a uniformly distributed load. The functionally graded face sheets were bonded to the homogeneous core using two thin layers of viscoelastic adhesive. Using the principle of virtual work, the governing equations were derived and transformed into the Laplace domain. The displacement fields were then obtained by applying the Navier solution and converted back to the time domain using the numerical inverse Laplace transform. The results were verified through finite element analysis, showing good agreement between the two approaches. Both methods revealed that the in-plane and out-of-plane stress components remain almost constant across the adhesive thickness but have considerable magnitudes. Additionally, the maximum adhesive planar stresses σ and τ are highly dependent on the magnitude of the adhesive elastic modulus, power index, and viscoelastic properties of the adhesive layer. Therefore, it was concluded that for a safe design in thin sandwich plates, the presence of viscoelastic adhesive layers must be considered in the formulation and their effect should not be ignored. 

Total hip joint replacement has problems, one of the most important of which is the stress shield phenomenon and weak bone growth. When the modulus of elasticity of the prosthesis is higher than that of the bone, most of the physiological load is transferred to the implant and the bone deteriorates. The solution to minimize it and strengthen bone growth is to use materials with elasticity modulus close to bone for prosthesis, and functionally graded materials (FGM) with porosity have shown better results than other materials. In this article, the model of cylinder and prosthesis based on ISO 7206-4 and the model of prosthesis and bone are used, and the results of applied stresses, stiffness of prostheses, and micromovements between prosthesis and bone are analyzed by the finite element method. The superiority of this study compared to previous studies is the use of prosthetic and cylinder models for different geometries and the investigation of micromovements and its effect on bone growth. The results show that the use of porous FGM prostheses for each different prosthesis geometry is effective in reducing the stress shield and bone growth.

In this study, the damage behavior of concrete under projectile impact is investigated. Thus, Johnson Holmquist brittle damage model, which is widely used to model penetration phenomenon, is chosen as the basic model. In order to more accurately predict the behavior of the material, a modified model is proposed by considering the new relationship for the effect of rate on the strength of the basic structural model. In the first step, the concepts of the basic model are expressed. Then, the formulation of the damage model is extracted and algorithm of the model for numerical simulation to solve it are presented. In order to implement and validate the algorithm, a subroutine is written in Fortran programming language based on the finite element method to simulate the damage process. In the following, using the developed model, the impact of the projectile on reinforced concrete is investigated. The model is verified by comparing the numerical and experimental results in the literatures. Numerical simulations using the proposed model show a good compatibility between simplicity and accuracy for calculations of concrete slabs under the impact of airborne projectile.

Composite materials are of great interest due to their exceptional strength, hardness-to-density ratio, high corrosion resistance, and low weight. One of the suitable methods for making composite pipes is using the extrusion process. Extrusion is a plastic deformation process that due to the compressive state of stress in extrusion, materials with low plasticity can be formed by this method. This article deals with the experimental-numerical investigation of extrusion, from various methods of forming process. Extrusion is done on a composite tube using aluminum and magnesium alloys. Aluminum is used due to its strength compared to high weight, excellent malleability, and magnesium due to the lightest structural metal, the lowest density among structural materials, machining, welding and casting capabilities, as well as high specific strength. The mentioned process was tested at different extrusion ratio, temperature and speed, and the effect of different process parameters on the properties of the extruded product was investigated. Then the process was simulated in the software and the experimental results obtained from the laboratory work and the numerical results obtained from the simulation were compared and validated with each other and the error percentage between the graphs of the experimental and numerical results was examined.

In this study, an analytical solution has been developed to examine the mechanical behavior of an incompressible functionally graded hyperelastic cylinder subjected to simultaneous extension and torsion. The recently proposed exp-exp strain energy density is employed to predict the behavior of hyperelastic material, and its related material parameters are assumed to vary along the radial direction in an exponential fashion. Finite element analysis is conducted by preparing a user-defined UHYPER subroutine in ABAQUS to evaluate the proposed analytical solutions. FEM results and those of the analytical solution are in good agreement for various stretches and twists and reveal that the form of stress distributions and the maximum stress depend on the exponential power in the material variation function. In contrast to axial stretch, the effect of twist on the distribution of longitudinal stress is more complicated, and for large twists, two extrema in the stress distribution plot are observed, which move toward the center and outer surface of the cylinder on further twisting. Moreover, the longitudinal stress controls the variation of von-Mises and strain energy density throughout the radial direction. Additionally, considering an axial stretch, a point is identified where the axial force arising from torsion is compressive for stretches below this value, and it brings about the cylinder to elongate under twisting. However, this part of the total axial force varies from a tension state to a compression one for larger stretches, i.e., by increasing the twist, the cylinder first tends to shorten and then elongates on further twisting.

In this research, the impact strength of functionally graded epoxy/graphene nanocomposite have been investigated. First, the samples were made for uniform and functionally graded distributions. Then, the distribution of nanoparticles has been investigated using a scanning electron microscope. Based on this investigation for uniform distribution up to 1.5% by weight of graphene nanoparticles, no signs of agglomerated particles were found. In addition, imaging was also done for the functionally graded sample and it was observed that the boundary of the layers is completely connected. Then the samples were subjected to Izod impact test and it was observed that for uniform distribution, the amount of energy absorption increased up to 1% by weight of graphene nanoparticles and then for the sample with 1.5% by weight of graphene nanoparticles, its value started to reduces. To validate the accuracy of the obtained results, modeling has been done for the mentioned samples using the finite element method and the obtained results have been compared with the experimental results.