Finite Element Concept Research Articles

UNVEILING THE INFLUENCE OF ONE-LEG STANCE AND STANDING UP FROM A CHAIR ON HUMAN HIP JOINT PROSTHESIS USING FINITE ELEMENT CONCEPTS

The hip joint plays an important role in providing stability to the human body. Factors such as aging, wear, and tear, make the hip joint degenerate and, in such cases, the same to be replaced through hip arthroplasty surgeries. The background of this study aims to investigate the contact consequence between the artificial femoral head and the acetabular cup for different bearing couples during one-leg stance and standing up from a chair, utilizing the finite element method. The three-dimensional finite dynamic contact model has been developed with different material combinations. The results obtained by the present finite element model align well with the previously available literature. The parameters investigated include maximum von Mises stress, maximum contact pressure and deformation for different material combinations. The results reveal that the pair i.e., Alumina on Ultra-high molecular weight polyethylene (UHMWPE) exhibits lower contact pressure, von Mises Stress and deformation. Therefore, the material pair i.e., Alumina on UHMWPE can be employed in the Total hip replacement (THR) to mitigate contact consequences under both static and dynamic loading conditions, thereby enhancing the durability of the artificial joints.

Finite element analysis-A biomechanical tool in orthodontics

In orthodontic research, the finite element method (FEM) has been widely used as an engineering resource for calculating the stress and deformation of complex structures. Applying the FEM can predict the graphic representation of these tissue responses through the observation of areas of stress created by applied orthodontic mechanics. This method has the advantage of being non-invasive, accurate, and providing quantitative and detailed data on the physiological reactions possible to occur in tissues. The purpose of this article is to review and discuss the steps involved in applying the concept of finite elements and how they can be used in orthodontics. The stress distribution at the interface between the alveolar bone and the periodontal ligament, as well as the shifting trend in different tooth movement types while employing different kinds of orthodontic devices, may both be assessed using FEM. For this reason, expertise with certain software is required. Despite the drawbacks of other experimental techniques, FEM is a crucial technique for addressing inquiries regarding tooth movement.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РАСПРОСТРАНЕНИЯ ВИБРАЦИЙ В ТОНКОСТЕННЫХ КАРКАСИРОВАННЫХ КОНСТРУКЦИЯХ. 2. КОНЕЧНО-ЭЛЕМЕНТНЫЕ МОДЕЛИ И ЧИСЛЕННЫЕ ЭКСПЕРИМЕНТЫ

Based on the refined S.P. Timoshenko shear model, one-dimensional finite elements for modeling the dynamic response of flat rods with clamped section of finite length on one of the front faces have been constructed. To analyze their stationary dynamic response under harmonic external action, a system of resolving equations in a complex form is formed. Three models of kinematic conjugation of clamped and free sections of rods are developed using the equation of connection between the rotation angle of the cross section and axial displacement at the boundary between the marked parts of the rod, the transitional finite element, and the concept of a single finite element with nodes located on one of its front faces. It is noted that for practical implementation, the most convenient model is one that uses a single finite element to represent fixed and free sections of the rod. On the basis of the noted model, a finite element solution of the problem of transverse bending vibrations of a cantilevered flat rod under vibration loading conditions by a periodic axial force applied to the end section of a clamped section of finite length, as well as the problem of transverse bending vibrations of a flat rod with two free ends and clamped length section between them under vibration loading by a transverse force on one of the free ends of the rod was found. The results of the finite element solution of the noted two problems are in good agreement with the previously obtained exact analytical solutions found on the basis of the S.P. Timoshenko shear model. The presence of a significant transformation of the parameters of the stress-strain state of the considered rods during the transition through the boundary from free to the clamped length areas on one of the face surfaces is noted.

Tribological behavior of zirconia-toughened alumina (ZTA) against Ti6Al4V under different bio-lubricants in hip prosthesis using experimental and finite element concepts

The present study investigated the tribological behaviour of zirconia toughened alumina (ZTA) against titanium alloy (Ti6Al4V) grade 5 material. Four loading conditions (15, 20, 25 and 30 N) with five different bio-lubricants include saline solution, Phosphate buffered saline, Ringer’s solution, Distilled water and Sesame oil were utilized to compute the friction and wear coefficients for a sliding distance of 10 km using ball-on-disc tribometer. Further submodeling finite element technique was used to estimate the contact pressure developed for normal walking equivalent to 2 years of implant’s life. The friction and wear coefficient values for sesame oil were found to be minimum among different loading and lubrication conditions. Also, the minimum wear was obtained for sesame oil bio-lubricant for normal walking activity. The obtained results suggested that sesame oil could improve tribological behavior as a bio-lubricant for ZTA-Ti6Al4V combination.

A non-homogeneous multi-material topology optimization approach for functionally graded structures with cracks

This article presents an effective non–homogeneous multi-material topology optimization paradigm for functionally graded (FG) structures, considering both cracked and non-cracked cases for the first time. For that aim, an enrichment finite element concept known as the extended finite element method (X-FEM) is employed to analyze strong discontinuity states’ critical mechanical behavior. The preconditioned block-conjugate gradient (pb-CG) is considered to deal with the X-FEM’s natural block system form for saving computational efforts. In addition, a block Gauss–Seidel-based alternating active-phase algorithm is utilized to convert a multiphase topology optimization problem subjected to multiple constraints to many binary phase topology optimization sub-problems with only one constraint. Consequently, the current topology optimization methodology can dramatically reduce the number of design variables regardless of the number of material phases. Optimality Criteria (OC) optimizer is then utilized to update optimized design variables for such sub-problems. The study formulates in great detail mathematical expressions for topology optimization of cracked structures with multiple FG materials. Several numerical examples are tested to verify the efficiency and reliability of the current paradigm.

K-Version of Finite Element Method for BVPs and IVPs

The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher order global differentiability approximations (HGDA/DG) are always p-version hierarchical that permit use of any desired p-level without effecting global differentiability. HGDA/DG are true Ci, Cij, Cijk, hence the dofs at the nonhierarchical nodes of the elements are transformable between natural and physical coordinate spaces using calculus. This is not the case with tensor product higher order continuity elements discussed in this paper, thus confirming that the tensor product approximations are not true Ci, Cijk, Cijk approximations. It is shown that isogeometric analysis for a domain with more than one patch can only yield solutions of class C0. This method has no concept of finite elements and local approximations, just patches. It is shown that compariso of this method with k-version of the finite element method is meaningless. Model problem studies in R2 establish accuracy and superior convergence characteristics of true Cijp-version hierarchical local approximations presented in this paper over tensor product approximations. Convergence characteristics of p-convergence, k-convergence and pk-convergence are illustrated for self adjoint, non-self adjoint and non-linear differential operators in BVPs. It is demonstrated that h, p and k are three independent parameters in all finite element computations. Tensor product local approximations and other published works on k-version and their limitations are discussed in the paper and are compared with present work.

Inverse problem techniques for multiple crack detection in 2D elastic continua based on extended finite element concepts

Two efficient methods are presented to detect multiple cracks in 2D elastic bodies, based on the insights from Extended Finite Element. Adetection mesh is assigned to the cracked body and the responses are measured at the nodes. A finite element model with the same mesh is used to represent the uncracked state of the physical body. In the first method which is called Crack Detection based on Residual Error (CDRE), the residual error norm is calculated based on the uncracked body stiffness matrix and the cracked body responses. The contour of the error norm would show the crack pattern; the method is computationally efficient. In the second method that is coined as Crack Detection based on Stiffness Residual (CDSR), the crack locations are found based on the difference between the stiffness matrix of the cracked body and the uncracked body. The stiffness matrix of the cracked body is found by solving a dynamic inverse problem based on a modified Tikhonov regularization. The efficiency and accuracy of the identification method are enhanced by predicting the crack pattern by the CDRE method. Several examples are presented to show the accuracy and robustness of the methods in the presence of high noise levels.

Nonlinear dynamic simulation of cable based structures interacting with sliding objects using the concept of macro element

This paper presents the formulation of a finite element enclosing a specific internal mechanical equilibrium in order to model cable-based structures in dynamics conditions. It is based on the concept of macro finite element which allows embedding complex mechanical systems solved inside the element boundaries. A significant advantage is to allow an easy implementation within classical commercial codes. The proposed macro finite element describes a cable interacting with a sliding object assimilated to a punctual mass where friction can be accounted for. The dynamic response is described by a model developed within the framework of the DEM (Discrete Element Method) where geometrical nonlinearity (large displacements) is considered. A model combining the proposed macro finite element and a classical linear truss finite element is presented in order to validate its implementation. Finally, illustrative examples are presented. First, a cable yarning system is considered. The effect of friction and of the bending stiffness of the posts on the overall kinematics and force within the system are explored. Then the vulnerability of a cable-stayed bridge to earthquake is explored accounting for guy ropes failure.

Soil-structure interaction effects on the seismic performance of frame structures

In this work, a numerical attempt has been elaborated to study the effects of soil properties, seismic impact and interaction between frame structure and soil foundation. The frame, soil and interface continuum have been modeled by using the finite element concept. In this approach, a numerical program has been established based on the direct method to analyze the soil-structure interaction under seismic loading. Adding, the developed thinlayer interface element ensuring the incompatibility of degrees of freedom between frame and soil elements is incorporated. Obtained results lead to explain (1) the influence of the soil-structure interaction on the seismic response of the frame structure and interface media, (2) the time history deflection of the superstructure and interface medium under seismic loading, (3) the effect of the interaction factor of soil-structure interaction on the seismic behavior of the interface medium and frame structure and (4) the earthquake intensity on the seismic damage. Lateral displacements at the top of the frame and at the interface level, and shear stresses at the contact between the foundation and structure are plotted and commented.

A hybrid boundary element-statistical energy analysis for the mid-frequency vibration of vibro-acoustic systems

Based on the concept of hybrid Finite Element (FE) analysis and Statistical Energy Analysis (SEA), a new hybrid method is developed for the mid-frequency vibration of vibro-acoustic systems. The Boundary Element (BE) method is used to describe the motion of a deterministic acoustic cavity. By enforcing the continuity conditions of displacement and velocity at the coupling interface, the dynamic coupling between the deterministic acoustic cavity and the statistical structure described by SEA is established. Then, a hybrid BE-SEA method for the mid-frequency vibration of vibro-acoustic systems is proposed. Post-processing provides formulations for calculating the sound pressure at points inside the acoustic cavity. Due to the nature of the BE method for acoustics, the proposed method not only has few degrees of freedom, but also automatically satisfies the Sommerfeld radiation condition at infinity for exterior acoustics problems. A numerical example compares results from the proposed hybrid BE-SEA method with those from the hybrid FE-SEA method and Monte Carlo simulation. The comparison illustrates that the proposed method gives good predictions for the mid-frequency behavior of vibro-acoustic systems and has the fewest degrees of freedom.

Failure Analysis of Composite Material Under External Hydrostatic Pressure: A Nonlinear Approach

This current study reports on comparison of nonlinear buckling behaviour of composite material under external hydrostatic pressure using finite element concept. Triaxial failure analysis has been employed at micro level to predict the damage behaviour and failure envelopes of polymer carbon-fiber reinforced composite involving thickness stresses. In addition, a buckling pressure equation based on ASME codes customized to IM7/8552 composite material was also presented. Finite element analysis using solid 3D shell element 190 with finite strain for IM7/8552 composite material have been performed in order investigate the validity of finite element method. Pre and post failure material nonlinearity in composite material has been discussed. The scope of present study is directed towards proposing the nonlinear constituent failure criteria and inelastic buckling behaviour of composite material at hydrostatic pressure. Furthermore, theoretical studies were done in conjunction with analytical studies to verify numerical analysis. It was found that IM7/8552 has failed due to its material nonlinearity having orthotropic properties. Optimal and accurate convergence in solution was observed and finite element analysis results are validated successfully. It can be concluded that there was significant increase in the mechanical properties as a function of hydrostatic pressure ranging from 0.13 to 1.20%. Allowable buckling pressure is anticipated by thickness to diameter ratio focuses geometric nonlinearity in material. The ASME equation and Windenburg equation (ABS) reveals in good prediction of design factor (∼ 3.5) for allowable buckling pressure. The progressive damage analysis showed finite element analysis and theoretical results are in agreement. The further scope of this study involves in development in failure constituent criteria with new damage analysis incorporating pressure and low temperature effects.

Mechanical Behavior of Metal under Hydrostatic Pressure and Low Temperature

The current work describes the behavior of metal under hydrostatic pressure and low temperature using finite element concept. This study was carried out in three stages: modelling, analysis and post processing. Structural steel and aluminum are tested at 600 bar pressure and 4°C temperature. Solid model of cylindrical shape having internal diameter 420 mm and thickness 25 mm was created and same was investigated for stress analysis using ANSYS 17.2 APDL emphasizing on hydrostatic behavior. Failure criterion is based on maximum stress to determine the onset of damage in material. In post processing phase, the material was checked for deformation and equivalent Von-Mises stresses developed around the material. The objective of this present paper is of two fold. Firstly the investigation of metal under high pressure through stress analysis is carried out followed by metallographic studies. The stress analysis results suggest that metals like steel which has BCC structure shows the remarkable decrease in ductility over the range of temperature. The maximum Von Mises stresses that the material can with stand were 65.14 MPa and 56.38 MPa for structural steel and aluminum respectively and revealed having high factor of safety for desired applications. It can be said that aluminum having FCC crystal structure are stiff and ductile even at low subzero temperature. The theoretical calculations are done and they are in agreement with the experimental results. It can be anticipated that influence of high pressure and low temperature can be criticized by two factors in terms of flow strength and fracture strength of metal. Ductile to Brittle Transition Temperature (DBTT) plays a vital role and can be considered as a measure of behavior of metal under high pressure and low temperature. So, it revels that the crystal structures of metals is the major factor which affects the behavior of metal which eventually affect the ductility and toughness of metal when subjected to high pressure and low temperature operations. However, in thick material the question of structural discontinuity and stress concentration is still regarded as open for further scope of study.

A multi-level damage and creep behaviour of material subjected to high pressure: metal versus composite – A micromechanics approach

This current study reports on multi-level damage and creep behaviour of metal and composite material under external high pressure using finite element concept. A fatigue damage model with microcracks with improper interface has been portrayed in the present investigation. In addition, the overall elastic properties and damage evaluation are also studied and comparative study of mechanical properties has been outlined. Further thermo-elastic creep response of materials based on Norton’s law is also presented. The results showed that the proposed nonlinear constitutive model and overall elastic damage behaviour of composite material are in agreement. Implemented nonlinear constitutive model is secured by comparing predicted stress–strain curves with experimental data available in the past literature under uniaxial tension. The time-dependent behaviour creep stresses and displacements are studied and plotted. The analysis provides significant new insights of micromechanical damage, creep and collapse behaviour of composite material. For the structural composites, some notable techniques have been developed over the past three decades; review of these techniques is also outlined here in this paper and state of art is established together with insights for upcoming development.

Modeling the closing behavior of a smart hydrogel micro-valve

Smart hydrogel micro-valves are essential components of micro-chemo-mechanical fluid systems. These valves are based on phase-changeable polymers. They can open and close micro-fluidic channels depending on the chemical concentration or the temperature in the fluid. A concept of finite element–based modeling in combination with network methods to simulate concentration-triggered, phase-changeable hydrogels is proposed. We introduce a temperature domain as a replication domain to substitute insufficiently implemented domains. With the used simulation tools, problems are highlighted and their solutions are presented. The computed parameters of such valves are included in a circuit representation, which is capable of efficiently computing large-scale micro-fluidic systems. These methods will help predict, visualize, and understand polymeric swelling behavior as well as the performance of large-scale chip applications before any complex experiment is performed.

An effective crack tip region finite element sub-model for fracture mechanics analysis

Purpose: To create an effective in engineering strength calculation three-dimensional submodel of the near crack tip region in solids for hi-fidelity analysis of their stress-strain state by the finite element method. Design/methodology/approach: To create a volume near the crack tip, regular threedimensional 20-node prismatic isoparametric elements and 15-node special elements with edge length of 12.5 μm with shifted nodes in order to simulate the singularity of stress at the crack tip were used. Using these two types of elements, a cylindrical fragment of diameter of 100 μm was built. In its base is a 16-vertex polygon, and its axis is the crack front line. In the radial direction the size of the elements was smoothly enlarged by creating of 5 circular layers of elements, and in the axial direction 8 layers were created. For convenience of the sub-model usage, the cylindrical fragment was completed by regular elements to a cubic form with edge size 400 μm. For the sub-model approbation, the full-scale three-dimensional models of standard specimens with cracks were built. The stress intensity factor K at normal tension was calculated assuming small scale yielding conditions in a plane between 4th and 5th layers of special elements on the basis of analysis of displacement fields near the crack tip. Findings: An effective three-dimensional sub-model of the near crack tip region is proposed. The sub-model was used to obtain the dependence of the stress intensity factor on the relative crack length at normal tension for four types of standard specimens. The obtained dependences show excellent correlation with known analytical solutions. Research limitations/implications: The concept of finite element meshing at threedimensional modelling of the near crack tip region for high-fidelity stress-strain state analysis was generalized. A sub-model of the near crack tip region was created and used to determine the stress intensity factor at normal tension of four types of standard specimens. It is shown that the proposed methodology is effective for precise analysis of the stressstrain state of solids with cracks within the framework of linear fracture mechanics. Practical implications: By applying the generalized approach and the proposed threedimensional sub-model of the near crack tip region, one can determine the stress-strain state of structure elements and machine parts when analysing their workability by the finite element method. Originality/value: An effective finite-element sub-model for the stress-strain state analysis in the vicinity of the crack tip within the framework of the linear fracture mechanics is proposed.

Parametric study and shrinkage modelling of natural rubber sheet drying using COMSOL multiphysics

Natural rubber is one of the major exporting cash crops in Thailand. Shrinkage in natural rubber sheet during drying creates uneven stresses in the rubber, hampers the quality and the water activity predisposes it to microbial activation. Hence, the effect of drying parameters on shrinkage has been considered in this work. The finite element concept coupled with the arbitrary Lagrangian-Eulerian (ALE) method was used to solve the two-dimensional coupled physics in the rubber sheet drying chamber and account for the shrinkage effect. The spatial domain (drying chamber), material domain (rubber sheet) was analysed. An isotropic linear elastic model was assumed for the rubber sheet for analysis. Three Case studies of different velocity, temperature, relative humidity and shrinkage coefficient were considered in the numerical study using COMSOL Multiphysics. It is concluded that increase in the operating parameters increases the shrinkage of the rubber. Therefore, rubber should dry at relatively lower operating parameters to improve its quality.

Closing and Unloading System Design of Medical Gas Cylinders

The unloading device medical gas cylinder often deforms and breaks in the production. For this purpose, an unloading device is designed in this paper, which describes its critical components and stress analysis in details. The finite element analysis has significant theoretical meaning and engineering application value to the structural analysis and design approach research of gas cylinders. In combination with the concept of finite element, the attentions and optimum selections are detailed in specific steps like ANSYS modeling, grids division, unit selection, loading and solving. Moreover, ANSYS software is used to simulate and calculate the stress on its link rod. Finally, the simulation result shows that, the link rod of unloading device meets the requirements in respect of stress and deformation.

FINITE ELEMENT TECHNIQUE FOR SOLUTION OF THERMO-CONTACT PROBLEMS AND ITS APPLICATION IN NUMERICAL ANALYSIS OF DEVICES WORKING WITH INDUCTION HEATING

Purpose. To develop an effective approach for the numerical solution of transient thermo-contact problems and present a typical example of its utilization regarding devices working on the principle of thermoelasticity produced by induction heating and specific technological processes intended for assembly and disassembly of systems containing shrink fits. Methodology. A finite element technique for solution of 2D multiphysics (electromagnetic, thermal and structural) problems is developed, taking into account temperature dependences of material properties and continuous variations of the contact surfaces. Modeling of the contact interaction between two parts is based on the concept of a special contact finite element having no thickness. The functional for the temperature problem is supplemented with components corresponding to the thermal conductivity of this contact layer. The heat generated due to mutual sliding of both parts can also be taken into account, but the heat capacity (specific heat) of the contact layer is neglected. Using a special 1D 4-node finite elements a system of equations for the description of the thermo-contact problem is obtained. Originality. Relatively simple analytical formulae for calculation of the contact thermal resistances occurring in specific parts of electrical machines are known. The paper offers an alternative approach for the numerical solution of transient thermo-contact problems based on the concept of a special 1D contact finite element having no thickness. Results. The presented technique is applied for the computer simulation of assembly and disassembly of a shrink fit using induction heating. Conclusions regarding the choice of technological modes are made. Comparative computations for drills made from hard alloy and alloyed tool steel are carried out.

PREDICTING THE WEAR OF SOFT-ON-HARD BEARING COUPLES FOR HUMAN HIP PROSTHESIS USING FINITE ELEMENT CONCEPTS

Wear of bearing couples is one of the major concerns in artificial hip implantation. To minimize the wear of hip bearing surfaces, several new materials have been introduced and tested including metal-on-metal, ceramic-on-ceramic and hard-on-hard combinations. The present study involves prediction of wear on ultra-high molecular weight polyethylene (UHMWPE) cup against Co–Cr, alumina and zirconia femoral head by applying the three-dimensional (3D) physiological loads as well as angular motions on these bearing couples to calculate the contact pressure using finite element concepts. The linear and volumetric wear of bearing surfaces increase with increase in gait cycles. Overall, the Zirconia–UHMWPE combination showed least wear, when compared with Alumina–UHMWPE and Co–Cr–UHMWPE combinations. The present study also revealed that the Zirconia–UHMWPE combinations showed less volumetric wear than the Alumina–Alumina bearing which is at present used in artificial hip resurfacements.

Description of the local series resistance of real solar cells by separate horizontal and vertical components

All previous concepts for describing the effective local series resistance of really existing solar cells, as it can be measured e.g. by luminescence imaging, try to describe it by a single local number. In solar cells showing an inhomogeneous saturation current density, this results in different series resistance images for the dark and illuminated case. The reason is the distributed character of the series resistance and the different diode current profiles under these different conditions. In this work the well-known finite element concept is used for describing a solar cell, which contains separate resistors carrying horizontal and vertical currents. A strategy is proposed how to fit these resistors to results of electroluminescence and lock-in thermography images of a real solar cell, leading to separate images of the local horizontal grid resistance, which may also show broken gridlines, and the local vertical׳lumped emitter contact resistance’. The latter lumps all resistive inhomogeneities of the cell, caused by a possibly inhomogeneous contact-, emitter-, grid-, bulk-, and back contact resistance. It will be shown that this description of the local series resistance reasonably describes both the dark and illuminated case, even in inhomogeneous multicrystalline silicon solar cells.