Stress analysis, finite element method

Experimental and numerical analysis methods have both been used to analyze the effects of post-core system. Since experimental methods may be too time consuming, expensive and require sophisticated procedure with coarse results, numerical analysis provides an effective tool. For numerical analysis, finite element method (FEM) was normally employed. Several studies investigated stress distribution in... 

The AUGUR information on defect configuration is used to develop the three-dimensional solid model of damaged pipeline weldment by the use of geometry editor. The editor options provide by easy way creation and changing of the solid model. This model is used for fracture analysis by finite element method with appropriate cross-section stress distribution and external loads. 

Although many interface models have been given so far, they are too qualitative and we can hardly connect them to the mechanics and mechanism of carbon black reinforcement of rubbers. On the other hand, many kinds of theories have also been proposed to explain the phenomena, but most of them deal only with a part of the phenomena and they could not totally answer the above four questions. The author has proposed a new interface model and theory to understand the mechanics and mechanism of carbon black reinforcement of rubbers based on the finite element method (FEM) stress analysis of the filled system, in journals and a book. In the new model and theory, the importance of carbon gel (bound rubber) in carbon black reinforcement of rubbers is emphasized repeatedly. Actually, it is not too much to say that the existence of bound rubber and its changeable and deformable characters depending on the magnitude of extension are the essence of carbon black reinforcement of rubbers. 

Finite element methods (FEM) are capable of incorporating complex variations in materia stresses in the time varying response. While these methods are widely available, they are quite complex and, in many cases, their use is not warranted due to uncertainties in blast load prediction. The dynamic material properties presented in this section can be used in FEM calculations however, the simplified response limits in the next section may not be suitable. Most FEM codes contain complex failure models which are better indicators of acceptable response. See Chapter 6, Dynamic Analysis Methods, for additional information. 

Stress calculations are carried out by the finite element method. Here, the commercial finite method code ABAQUS (Hibbit, Karlsson, and Sorensen, Inc.) is used. Other codes such as MARC, ANSYS are also available. To calculate the stresses precisely, appropriate meshes and elements have to be used. 2D and shell meshes are not enough to figure out stress states of SOFC cells precisely, and thus 3D meshes is suitable for the stress calculation. Since the division of a model into individual tetrahedral sometimes faces difficulties of visualization and could easily lead to errors in numbering, eight-comered brick elements are convenient for the use. The element type used for the stress simulation here is three-dimensional solid elements of an 8-node linear brick. In the coupled calculation between the thermo-fluid calculation and the stress calculation a same mesh model have to be used. Consequently same discrete 3D meshes used for the thermo-fluid analysis are employed for the stress calculation. Using ABAQUS, the deformations and stresses in a material under a load are calculated. Besides this treatment, the initial and final conditions of models can be set as the boundary conditions and the structural change can thus be treated. 

O.C. Zienkiewicz. Finite Element Methods in Stress Analysis, chapter 13 Iso-parametric and associate elements families for two and three dimensional analysis. Tapir Press, Trondheim, 1969. 

The indirect analytical nondestructive evaluation methods of interest are thermal analysis, finite element stress analysis, strain gauging, photoelasticity and brittle coatings. 

Other methods available for nondestructive evaluations are indirect in nature, but may be useful in certain situations. These methods will only be discussed in a cursory fashion and more detailed aspects can be obtained from the literature. It is useful to note that stress in any structure plays a vital role, and that the methods involved in determining stress in an engineering component or structure in the process conditions is of vital importance. The methods used in determining stress are finite element stress analysis, strain gaging, the photoelastic method and brittle coatings. 

In any structure the entire structure responds to mechanical or thermal loads. It is also necessary to bear in mind that any structure will also experience localized stress concentrations at points of contact or separation in the structure. These points of contact or separation are sites susceptible to damage, cracking or failure initiation. Stress analysis using the finite element method in structures which are bolted, mating surfaces, vessels... 

Although the Finite Element Method is still not very common for calculating the static strength of a vessel, it became a standard tool for computation of peak stresses (Figure 1) for fatigue analysis. 

This chapter also does not consider the analysis of stresses around piping, connections, supports, attachments, and so on. While the experienced engineer can design a vessel to prevent failure at these locations, accurate analysis requires elaborate techniques such as the Finite Element Method. This method has been applied with great success to analyze complex vessels such as nuclear reaction vessels. The reader should consult appropriate references if he wishes to pursue this area. References 2 and 3 are basic textbooks in the field of finite element analysis. 

Obviously, quantitative modelling of stress-assisted hydrogen diffusion requires the stress field in a testpiece of interest to be known. Even for rather simple cases, such as a notched bar being considered here, neither the exact solutions nor the closed form ones are usually available. Thus, one must count on some sort of the numerical solution of the mechanical portion of the coupled problem of the stress-assisted diffusion. The finite element method (FEM) approach, well-developed for both linear and nonlinear analyses of deformable solid mechanics, is a right choice to perform the stress analysis as a prerequisite for diffusion calculations. 

Figure 8.63. Finite element method stress analysis around the particulate in polystyrene, (a) the system with dispersed softer particles, (h) the system with dispersed harder particles, (c) the system with dispersed particles having a peeling layer (adsorbed polymer). [Adapted, by permission, from Mitsui S, Kihara H, Yoshimi S, Okamoto Y, Polym. Engng. Sci., 36, No.l7, 1996, 2241-6.]...

A computational design procedure of a thermoelectric power device using Functionally Graded Materials (FGM) is presented. A model of thermoelectric materials is presented for transport properties of heavily doped semiconductors, electron and phonon transport coefficients are calculated using band theory. And, a procedure of an elastic thermal stress analysis is presented on a functionally graded thermoelectric device by two-dimensional finite element technique. First, temperature distributions are calculated by two-dimensional non-linear finite element method based on expressions of thermoelectric phenomenon. Next, using temperature distributions, thermal stress distributions are computed by two-dimensional elastic finite element analysis. 

Thermoelectric analysis and thermal stress analysis are performed on single-stage thermoelectric generator by the finite element method. An analysis model is shown in Figure 5. The device is... 

There has been the question why the TPV materials with ductile thermoplastic matrix display rubber elasticity. Several models have been suggested to answer this question (41 7). Inoue group first analyzed the origin of mbber elasticity in TPVs (43). They constructed a two-dimensional model with four EPDM mbber inclusions in ductile PP matrix and carried out the elastic-plastic analysis on the deformation mechanism of the two-phase system by finite-element method (FEM). The FEM analysis revealed that, even at highly deformed states at which almost the whole matrix has been yielded by the stress concentration, the ligament matrix between mbber inclusions in the stretching direction is locally preserved within an elastic limit and it acts as an in-situ formed adhesive for interconnecting mbber particles. 

For the basic equations of coupled stress-flow analysis mentioned above, it is very difficult to solve them in closed-form. The transposition method of progression and integration can only be applied for problems of boundary value problems of simple geometry and boundary conditions. Therefore the finite element method (FEM) is used to solve the coupled partial differential equations in this paper. 

At present, the finite-element method is the main method, which is carried out in the analysis of stress on rocks. It is an effective numerical way that grows more available with the development of computers. The essence of the finite element is to idealize the continuum with infinite degree of freedom into the unit with limited degree of freedom and simplify the problem to a structure, which is suitable for numerical solutions. 

Clough RW (1960) The finite element method in plane stress analysis. In Proceedings of ASCE 2nd conference on electronic computation. Conference papers American Society of Civil Engineers 2nd conference on electronic computation, 8-9 Sept 1960, Pittsburgh Courant R (1942) Variational methods for the solution of problems of equilibrium and vibrations. Bull Amer Math Soc 49 1-23... 

Currently, numerical methods are most used to solve heat transmission problems. The method of Finite Differences is being substituted by the Finite Element Method. Most Finite Element based mechanical calculation codes include the Thermal Analysis. The temperature distribution obtained from the thermal calculation is used as a load input to the mechanical stress and deformation problem. For that, the temperatures at the nodes are transformed into initial strain by means of the equation... 

Reynolds CW (1987) Flocks, herds and schools a distributed behavioral model. Computer Graphics, ACM SIGGRAPH 87 Conference Proceedings Treanor G, Hinds BK (2000) Analysis of stresses in micro-drills using the finite element method. Int J Mach Tools Manufact 40(10) 1443-1456... 

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