Coupled Rayleigh-Ritz/finite element structural analysis using penalty function method

Objective To explore the establishment of 3D thoracic model by finite element methods, and study the mechanical mechanism of minimally invasive surgery for correcting the chest wall deformity, and provide personalized surgery solution in the future. Methods According to admission and exclusion criteria, we selected 10 cases of pectus carinatum that received chest CT scan. The finite element model of pectus carinatum was established and analyzed by Mimics, ABAQUS, etc. The validity of finite element method for chest wall was verified by comparing the sternal displacement between the simulated values and actual values with the same force. Results The 3D finite element model of pectus carinatum was successfully established and analyzed. The stress distribution of the 10 cases in the posterior ribs was mainly in the 1-6 ribs on both sides, mostly concentrated in the 4th to 6th ribs, and the stress was symmetrical on both sides. Statistical analysis showed that the displacement value of the sternum was correlated, and the validity of the model was verified. Conclusion Mimics, ABAQUS and other finite element modeling and analysis software can effectively establish the thoracic 3D finite element model and mechanical analysis, which can help the further development of personalized minimally invasive surgery for correcting chest wall deformities. Key words: Pectus carinatum; Chest wall deformity; Finite element analysis

Real-world groundwater modeling deals with heterogeneous and anisotropic aquifer systems. Numerical models, particularly the finite difference and finite element methods, are extensively used for modeling such a complex aquifer system. The finite difference method is an age-old straightforward approach, whereas the finite element method is more idealistic, relatively new, and has emerged as a popular approach. The unique advantages with the finite element method are (i) an irregular-shaped domain can be discretized into elements with a matching boundary, (ii) a node can be connected with the neighboring nodes in any direction. Thus, the finite element analysis allows water/solute to flow more freely toward the surrounding nodes along nodal links. On the other hand, the mathematical formulation of the finite element technique follows a set of rules step by step. Conventionally, this idealistic approach uses shape functions and integration techniques to develop element matrices, which, in turn, are assembled to form the global matrix. This conventional global matrix was found to be inconsistent with the basic partial differential equation representing the mass balance in a nodal domain as a control volume. As a result, the matrix solution, particularly for nonlinear problems (e.g., vadose zone flow, density dependent flow, and so forth) becomes unstable and computationally burdensome. To overcome the limitations of the conventional finite element method for real-world groundwater modeling, a new approach, called the direct-formulation finite element (DFFE) method, has been developed. In this approach, a two-dimensional model domain is discretized into triangular elements. Element matrices are formed directly based on flow principles and material properties of elements without using shape functions and integration process. The DFFE method is robust. The global matrix is consistent, and the solution is stable and efficient. The results obtained from this approach were found in a good agreement with that obtained from analytical and other widely used models.

Connecting rod is a major link inside of a internal combustion engine. It is the intermediate member between the piston and the crankshaft. Its primary function is to transmit the push and pull from the piston pin to the crank pin thus converting the reciprocating motion of piston in to rotary motion of the crank. In this paper a static analysis is conducted on a connecting rod of a single cylinder 4-stroke petrol engine. The model is developed using Solid modeling software i.e. PRO/E (creo-parametric). Further finite element analysis is done to determine the von-misses stresses shear stress and strains for the given loading conditions. Keywords - ANSYS Workbench, connecting rod, Finite Element analysis, PRO/E (creo-parametric). I. Introduction Connecting rod is among large volume production component in the internal combustion engine. It connects the piston to the crankshaft and is responsible for transferring power from the piston to the crankshaft and sending it in to transmission. They are different types of materials and production methods used in the creation of connecting rods. The major stresses induced in the connecting rod are a combination of axial and bending stresses in operation. The axial stresses are produced due to cylinder gas pressure (compressive only) and the inertia force arising in account of reciprocating action (both tensile as well as compressive), where as bending stresses are caused due to the centrifugal effects. It consists of a long shank, a small end and a big end. The cross-section of the shank may be rectangular, circular, tubular, I-section or H-section. Generally circular section is used for low speed engines while I-section is preferred for high speed engines. The most common type of manufacturing processes is casting, forging, and powdered metallurgy. Connecting rod is subjected to a complex state of loading. It undergoes high cyclic loads of the order of 10^8 to 10^9 cycles, which range from high compressive loads due to combustion, to high tensile loads due to inertia. Therefore, durability of this component is critical importance. Due to these factors, the connecting rod has been the topic of research for different aspects such as production technology, materials, performance, simulation, fatigue etc. Vivek.c.pathade et al(1) performed stress analysis of I.C Engine connecting rod by finite element method. They modeled connecting rod using pro/E Wildfire 4.0 and ANSYS Workbench 11.0 software. They reported from the theoretical and finite element analysis then the stresses induced in the small end of the connecting rod are greater than the stress induced at the big end. K.surdershn Kumar et al (2), reported on modeling and analysis of two wheeler connecting rod. In this connecting rod is replaced by aluminum reinforced with boron carbide for Suzuki GS150R motor bike. A parametric model of connecting rod is modeled using pro/E Wildfire 4.0. Analysis is carried out by using ANSYS software. They presented the results of materials and reported that the working factor of safety is nearer to theoretical factor of safety in aluminum boron carbide. Anil Kumar et al (3), presented the optimization of connecting rod parameters using CAE tools. They reported on optimizing weight and reducing inertia forces on the existing connecting rod, which is obtained by changing design variables in the existing connecting rod design. The model was developed in pro/E Wildfire 5.0 and then imported as a Para solid (xt) from in ANSYS Workbench. The stress was found maximum at the piston end. This can be reduced by increasing the material near the piston end. The weight of the connecting rod was also reduced by 0.004kg which was not significant but reduces the inertia forces. Suraj pal et al (4), reported on design evaluation and optimization of connecting rod parameters using Finite element method. Proper finite element model is developed using pro/E Wildfire 4.0. The weight of the connecting rod is also reduced by 0.477g. The stress is found maximum at the piston end so that material is increased in the stressed portion to reduce stress. Dr. S B Jaju et al (5), performed modeling and analysis of connecting rod of four stoke single cylinder engine for optimization of cost and material. Their study has dealt with two subjects first static load stress analysis of the connecting rod, and then second optimization for weight.

Investigation of the effects of allogeneic mesenchymal stem cells on bone union and regeneration in the necrosed bone by biomechanical test and the finite element method

This paper presents an efficient inverse analysis technique for the identification of an unknown boundary condition in a finite element method (FEM) on a small memory capacity machine such as a personal computer. The author has previously presented the FEM of inverse analysis introducing an inverse compliance matrix that uses an influence function into the stiffness matrix for the unknown boundary. Since the stiffness matrix of the FEM becomes singular, following two calculation processes are adopted: (1) a calculation process which obtains an approximate solution by decreasing the effect of the inverse compliance in the stiffness, and (2) an iterative calculation process computing a correct solution from the approximation using (1). First, a penalty function method is used to decrease the rank of a singular stiffness matrix in (1). Then, the number for computing LDU decomposed matrix becomes twice in comparison with fourth times in the previous paper. Next, an efficient calculation method is presented using an attack technique based on both accelerative moving lower and upper bounds in (2). Moreover, a zooming identification method is developed, owing to an improvement of node displacements on and near the edges. Therefore, this technique makes it possible to establish an efficient inverse analysis for the identification of the unknown boundary. Finally, the validity of the inverse analysis technique is confirmed from the numerical solution of a three-dimensional inverse finite element analysis model, as an example of an elastic structure with reinforced members under tension, carried out on a small memory capacity machine.

Magnetic field analysis using the finite element method in general requires current density to be a known quantity. An electric network, however, is usually driven by constant voltage sources and the currents are affected by the impedances not only in the circuit but also in the finite element analysis region which is connected to the circuit. Therefore, it is generally difficult to know the current density in advance. This paper proposes a general method for analyzing a magnetic field in an electric network. Expanding the signal flow graph (SFG) method makes possible the simultaneous analysis of an electric network and in its magnetic field; the network including the finite element analysis region is expressed by a SFG and the linear simultaneous equations of the SFG and those of the finite element method are combined. As a SFG can be constructed systematically for arbitrary network;the analyst need only prepare data regarding the connection of elements, their electrical characteristics, and the parameters of the finite element analysis region. In this paper, a two dimensional static magnetic field taking account of eddy current is considered and the proposed method is applied to the analyses of electromagnetic stirrer.

Finite element analysis has become the most popular technique for studying engineering structures in detail. It is particularly useful whenever the complexity of the geometry or of the loading is such that alternative methods are inappropriate. The finite element method is based on the premise that a complex structure can be broken down into finitely many smaller pieces (elements), the behaviour of each of which is known or can be postulated. These elements might then be assembled in some sense to model the behaviour of the structure. Intuitively this premise seems reasonable, but there are many important questions that need to be answered. In order to answer them it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. The approach that will be taken in this book is to develop the fundamental ideas and methodologies based on an intuitive engineering approach, and then to support them with appropriate mathematical proofs where necessary. It will rapidly become clear that the finite element method is an extremely powerful tool for the analysis of structures (and for other field problems), but that the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary. As stated above, many questions arise concerning finite element analysis. Some of these questions are associated with the fundamental mathematical formulations, some with numerical solution techniques, and others with the practical application of the method. In order to answer these questions, the engineer/analyst needs to understand both the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis programs is most likely to arise when the analyst is ignorant of engineering phenomena.

Objective To investigate effects of bone-resorptive lesion on stress distribution of femoral head and on progression in patients with osteonecrosis of the femoral head (ONFH). Methods From April 2014 to September 2018, a total of 155 femoral heads from 94 patients diagnosed with ARCO stage II and III ONFH were retrospectively reviewed, including 77 males and 17 females with aged 39.90±10.45 years old (ranged from 18-64 years). The hips were divided into two groups according to whether there were bone-resorptive lesions. Further, we compared whether there was statistical difference between the two groups in staging. Then, a case of ARCO II hip joint without bone-resorptive lesion was selected from the included patients. Six femoral head with different diameters of spherical bone-resorptive lesion of 5 mm, 7 mm, 10 mm, 14 mm, 18 mm, and 23 mm were simulated. The influence of bone-resorptive lesion on the stress distribution of necrotic area and a spherical shell extending 1 mm radially around the bone-resorptive lesion was investigated by finite element method in slow walking conditions. Results Of the 155 ONFH hips, 67 hips are complicated by bone-resorptive lesions, of which 17 were ARCO II, 50 were ARCO III. A total of 88 hips did not contain bone-resorptive lesions, of which 58 were ARCO II, ARCO III 30 cases. The proportion of ARCO stage II in the group with bone-resorptive lesions was significantly higher than that in the group without bone-resorptive lesions (χ2=25.03, P=0.000). The finite element stress distribution cloud diagram showed that there was a stress concentration area around the bone-resorptive lesions. The maximum von Mises stress around bone-resorptive lesions in the models that contained a synthetic bone-resorptive lesions were significantly higher than those reported in the matched, non-synthetic bone-resorptive lesions finite element models (t=3.139, P=0.026). The values for maximum von Mises stress around bone-resorptive lesions were 6.94±1.78 MPa and 5.01±0.35 MPa for the group with synthetic bone-resorptive lesions and the group non-synthetic bone-resorptive lesions, respectively. There was a positive correlation between the diameter of bone-resorptive lesions and the maximum and mean von Mises stress of necrotic areas as well as the maximum von Mises stress around bone-resorptive lesions. Conclusion Bone-resorptive lesions can increase the maximum stress and average stress in the necrotic area. The larger the bone-resorptive lesion, the more the stress increases. There is a stress concentration area around the bone-resorptive lesions, which may accelerate the collapse of the femoral head. Key words: Femur head necrosis; Bone resorption; Finite element analysis

Este trabajo propone un método de elementos finitos (FE) para calcular la profundidad de penetración por corrosión (rcrit) en las armaduras de acero, necesaria para originar la aparición de la primera grieta visible en el recubrimiento de hormigón. El análisis por FE se ha llevado a cabo utilizando el programa comercial ANSYS. El método de FE obtenido se ha desarrollado en función del espesor del recubrimiento de hormigón libre (C), el diámetro de la armadura (D), la longitud de la zona anódica (L), y el tipo de hormigón. Los resultados obtenidos muestran una gran influencia de la corrosión localizada (pequeñas zonas anódicas frente a grandes zonas catódicas) en la predicción del valor de rcrit. Esta influencia sólo puede ser analizada tridimensionalmente. El modelo de FE propuesto se validó utilizando datos de la bibliografía. La originalidad del procedimiento propuesto radica en la consideración de la dirección longitudinal en el análisis, para tener en cuenta la extensión de la zona anódica. El tipo de corrosión tiene una gran dependencia de la relación entre C/L, ocasionando corrosión uniforme para valores entre 0,02 < C/L < 0,1, y originando corrosión localizada para valores entre 0,5 < C/L < 4,0.

The effects of surface elasticity and surface viscoelasticity as well as surface tension on the deformation of solids with liquid inclusions are investigated using a finite element (FE) method. Both surface tension and surface elasticity stiffen the solids with liquid inclusions. The surface tension in elastic capillary number is replaced with surface Young’s modulus to define the second elastic capillary number. The aspect ratio of the included liquids is used to indicate the stiffening effect for both numbers. A smaller aspect ratio corresponds to a larger stiffening effect. In a typical FE analysis, when either number is 1 and the applied strain is 4%, the aspect ratio decreases by 7.4% due to surface tension and 2.6% due to surface elasticity. Compared to surface tension, surface elasticity has a similar but smaller influence on the deformation of solids with liquid inclusions. Extensive FE calculations are performed to establish the fitting formula for the aspect ratio as a function of elastic capillary number, the second elastic capillary number, and the applied strain. Surface viscoelasticity is modelled in the FE method by converting surface viscoelastic properties into the viscoelastic properties of the equivalent shell. The time-dependent aspect ratio due to surface viscoelasticity is presented and FE results show the same trend as those calculated from the approximated theory. The internal pressure of the included liquid is obtained from FE analysis and is compared with the theoretical estimation employing the Young–Laplace equation.

A constitutive theory, finite element formulation and topology optimization for anti-vibration rubber are presented. Many vibration isolators made of rubbers are operating under small oscillatory load superimposed on large static deformation. A~viscoelastic constitutive equation for rubber is proposed considering the influence of large static pre-deformation on the dynamic properties. The proposed model is derived through linearization of Simo's viscoelastic constitutive model and introduction of static deformation correction factor. And then the model is implemented in a finite element code to analyze the behavior of rubber elements under general loading conditions. Dynamic tests are performed in order to verify the model under multi-axial deformation. The computed results by the FEA code are compared with the experimental results and the suggested constitutive equation with static deformation correction factor shows good agreement with the test values. For the stability and low transmissibility of isolation systems, both static and dynamic performance must be concurrently considered in the design process. The continuum-based design sensitivity analyses (DSA) of both the static hyperelastic model and dynamic viscoelastic model are developed. And then the topology optimization methodology is used in order to generate the system layouts considering both the static and dynamic performance.

Analytical and finite element methods are employed to determine the contact pressure on the surface of a tissue being grasped by an endoscopic grasper, in Minimally Invasive Surgery (MIS). Normally, an endoscopic grasper is corrugated (teeth-like) in order to grasp slippery tissues. It is highly important to avoid damage to the tissues while grasping and manipulation during endoscopic surgery. Therefore, it is essential to determine the exact contact pressure on the surface of the tissue. To this end, initially a comprehensive closed form, finite element and experimental analysis of grasping contact pressure on viscoelastic materials which have similar properties as that of biological tissues is studied. The behavior of a grasper with wedge-like teeth, when pressed into a linear viscoelastic material is examined. Initially, a single wedge penetrating into a solid is studied and then is extended to the grasper. The elastic wedge indentation is the basis of the closed form analysis and the effects of time are included in the equations by considering the corresponding integral operator from viscoelastic stress-stain relations. In addition, a finite element analysis is carried out in Ansys-10 software. Finally, the experimental results are presented to validate both analytical and FEM results. The results of this study provide a closed form expression for grasping contact pressure force and contact area along with the variations of stress in tissue obtained through FEM analysis. The variation of contact pressure and the rate of growth of the contact area with time are presented.

New finite element study protocol: Clinical simulation of orthodontic tooth movement

Geometrically complex geological features, such as faults, cross stratified beds and large scale inclined strata, can have very significant effects on the flow of reservoir fluids. Standard finite difference methodology lacks the geometric flexibility required for modeling flow through or around such structures. Triangle based discretization methods, by contrast, offer an attractive means to discretize and simulate flow through geometrically complex features accurately. In this paper, a triangle based mixed finite element – finite volume technique for compositional reservoir simulation is developed. The formulation is of IMPES type and is applicable to three phase, multicomponent systems in two dimensions. Most previous mixed finite element formulations were restricted to two phase or fully miscible systems. The compositional approach presented here extends these earlier techniques though it retains the general structure of the more limited formulations. Specifically, the governing equations are cast in terms of a pressure equation and a series of component mass balance equations expressed in terms of the ‘total’ velocity. A triangle based mixed finite element method is applied to the solution of the pressure equation while a finite volume technique is employed for solution of the component mass balance equations. The overall methodology is particularly well suited for the modeling of flow through complex geological strata characterized by heterogeneous, generally anisotropic permeability fields. This is demonstrated explicitly through application of a preliminary implementation of the method to the simulation of flow through a faulted cross section with a complex permeability description. Extension of the formulation to the three dimensional case is also discussed.

One of the main causes of severe wear or crack initiation in wheel and rail is the contact stress due to wheel-rail contact. First, we obtain contact stress due to the rail mounting slope using the finite element method. Second, the shape design based on more reasonable contact stress analysis rather th~n a general Hertzian contact theory is investigated in order to reduce the contact stress. The optimum -design is performed using the simple 2-D finite element model and its results are verified by 311) finite element analysis.