Finite-Element Analyses

The name FEA refers to an object or structure to be modeled with a finite number of elements. FEA can be defined as a numerical technique, involving breaking a complex problem down into small subproblems, via computer models that can be solved by a computer. 

The key to effective FEA modeling is to concentrate element details at areas of highest stress. This approach produces maximum accuracy at the lowest cost. 

FEA with a computer analysis provides a means to theoretically predict the structural integrity of a product using mathematical geometry and load simulation. A stress analysis can be taken of finite sections for analysis of the forces and loads the part will experience in service. It generates an analysis that shows the force concentrations in the section and determines if the material and design shape selected will meet product performance requirements. 

In reviewing mechanical engineering analysis, one can perform using one or two approaches, namely analytical or experimental. Using the 

There are various analytical methods available to the designer using a CAD system. FEA and static and dynamic analysis are all commonly performed analytical methods available in CAD. FEA is a computer numerical analysis program used to solve the complex problems in many engineering and scientific fields, such as structural analysis (stress, deflection, vibration), thermal analysis (steady state and transient), and fluid dynamics analysis (laminar and turbulent flow). 

For purposes of illustration we restrict our attention to the two-dimensional problem, and introduce a Galerkin finite element approximation to the weak form (6.44) and (6.45). The unknown functions are the increment of displacement Au and the incremental excess pore pressure Ap. Introducing the global shape functions Na(x, y) =, N) and Nce(x, y) = -, N) corresponding to each 

Under the interpolation of an incremental displacement (6.46) the strain increment (6.38) is represented as 

6 Qassical Theory of Consolidation for Saturated Porous Media 

The increment of volumetric strain for a two-dimensional plane strain problem is 

By using the interpolation function (6.47) of the increment of pore pressure, its gradient V(A/ ) is represented as 

The opportunity for creative design by viewing many imaginative variations would be blunted if each variation introduced a new set of doubts as to its ability to withstand whatever stress might be applied. From this point of view the development of computer graphics has to be accompanied by an analysis technique capable of determining stress levels, regardless of the shape of the part. This need is met by finite element analysis [1, 2, 10-12, 62-68, 72, 381-84, 419-41]. 

Finite element analysis (FEA) is a computer-based technique for determining the stresses and deflections in a structure. Essentially, this method divides a structure into small elements with defined stress and deflection characteristics. The method is based on manipulating arrays of large matrix equations that can be realistically solved only by computer. Most often, FEA is performed with commercial programs. In many cases these programs require that the user know only how to properly prepare the program input. 

FEA is applicable in several types of analyses. The most common one is static analysis to solve for deflections, strains, and stresses in a structure that is under a constant set of applied loads. In FEA a material is generally assumed to be linear elastic, but nonlinear behavior such as plastic deformation, creep, and large deflections also are analyzed. The designer must be aware that as the degree of anisotropy increases the number of constants or moduli required to describe the material increases. 

Uncertainty about a material s properties, along with a questionable applicability of the simple analysis techniques generally used, provides justification for extensive end-use testing of plastic parts before approving them in a particular application. However, it should be noted that as the use of more FEA methods becomes common in plastic design, the ability of FEAs to handle anisotropic materials will demand greater understanding of the anisotropic nature of plastics. 

FEA does not replace testing rather, the two are complementary in nature. Testing supplies only one basic answer about a design—either pass or fail. It does not quantify results, because it is not possible to know from testing alone how close to the point of passing or failing a design actually exists. FEA does, however, provide information with which to quantify performance. 

Designing products is usually performed based on experience since most products only require a practical approach (Fig. 1-4). Experience is also used in producing new and complex shaped products usually with the required analytical evaluation that involves stress-strain characteristics of the plastic materials. Testing of prototypes and/or preliminary production products to meet performance requirements is a very viable approach used by many. 

With the computer hundreds of simultaneous equations can be solved that would take 

The first step in applying FEA is the construction of a model that breaks a component into simple standardized shapes or (usual term) elements located in space by a common coordinate grid system. The coordinate points of the element corners, or nodes, are the locations in the model where output data are provided. In some cases, special elements can also be used that provide additional nodes along their length or sides. Nodal stiffness properties are identified, arranged into matrices, and loaded into a computer where they are processed with certain applied loads and boundary conditions to calculate displacements and strains imposed by the loads (Appendix A PLASTICS DESIGN TOOLBOX). 

In this method, the modeling technique is critical because it establishes the structural locations where stresses will be evaluated. If a component is modeled inadequately for a given problem, the resulting computer analysis could be quite misleading in its prediction of areas of maximum strain and maximum deflection values. An inadequate model could be quite expensive in terms of computer time. 

A cost-effective model concentrates on the smallest elements at areas of highest stress. This configuration provides greater detail in areas of major stress and distortion, and minimizes computer time in analyzing regions of the component where stresses and local distortions are smaller. 

---

Pittman, J. F.T. and Nakazawa, S., 1984. Finite element analysis of polymer processing operations. In Pittman, J.F. T., Zienkiewicz, O.C., Wood, R.D. and Alexander, J. M. (eds), Num,erical Analysis of Forming Processes, Wiley, Chichester. 

Pittman, J.F.T. and Nakazawa, S., 1984. Finite element analysis of polymer processing... 

Kheshgi, H. S. and Scriven, L. E., 1985. Variable penalty method for finite element analysis of incompressible flow. Int. J. Numer. Methods Fluids 5, 785-803. 

Ghassemieli, E. and Nassehi, V., 2001c. Prediction of failure and fracture mechanisms of polymeric composites using finite element analysis. Part 2 liber reintorced composites. Poly. Compos. 22, 542-554. 

Nassehi, V. and Ghoreishy, M, H. R., 1998. Finite element analysis of mixing in partially filled twin blade internal mixers. Int. Polym. Process. XIII, 231 -238. 

The most frequently used modifications of the basic Gaussian elimination method in finite element analysis are the LU decomposition and frontal solution techniques. 

Irons, B, M., 1970. A frontal solution for finite element analysis, hit. J. Numer. Methods Eng. 2, 5-32,... 

F. Tabaddot, Finite Element Analysis of Tire eV Rubber Products, ContinuingEducation, The University of Akron, Akron, Ohio, 1984, Chapt. VI. 

S. E. Kistier and L. E. Scriven, "Finite Element Analysis of Dynamic Wetting for Curtain Coating at High Capillary Numbers," presented at... 

Many developers of software for finite-element analysis (18) provide drafting of pipelines and associated flow analysis. These companies include Algor, McAuto, MacNeal-Schwindler, and ElowDesign. In software, in-house developed pipe fittings are modularized and isometric views of the piping systems with three-dimensional detailing are now commonplace. 

Y. C. Pao, A First Course in Finite Element Analysis., AHyn and Bacon, Boston, 1986. 

To this day, balanced mechanical seals using o-rings are the standard in industry. Meehanical seals eontinue to evolve in sealing face technology, computer design, finite element analysis, cartridge designs, split seals, double or dual seals, and dry gas seals. 

The failure determining stresses are also often loeated in loeal regions of the eomponent and are not easily represented by standard stress analysis methods (Sehatz et al., 1974). Loads in two or more axes generally provide the greatest stresses, and should be resolved into prineipal stresses (Ireson et al., 1996). In statie failure theory, the error ean be represented by a eoeffieient of variation, and has been proposed as C =0.02. This margin of error inereases with dynamie models and for statie finite element analysis, the eoeffieient of variation is eited as Q = 0.05 (Smith, 1995 Ullman, 1992). 

Finite element analysis First party audits... 

For complex offshore structures or where foundations may be critical, finite-element analysis computer programs with dynamic simulation capability erm be used to evaluate foundation natural frequency and the forced vibration response. 

D. Givoli, J. E. Flaherty, M. S. Shephard. Parallel adaptive finite element analysis of viscous flows based on a combined compressible-incompressible formulation. Int J Numer Meth Heat and Fluid Flow 7 880, 1997. 

Strain gages may be applied to the test unit at all points where high stresses are anticipated, provided that the configuration of the units permits such techniques. The use of finite element analysis, models, brittle lacquer, etc., is recommended to confirm the proper location of strain gages. Three-element strain gages are recommended in critical areas to permit determination of the shear stresses and to eliminate the need for exact orientation of the gages. 

The major advance in fretting fatigue has been the finite element analysis... 

CADplus SOLID EDGE Advanced mechanical simulation via finite element analysis by Algor, Inc. Pittsburgh, PA www.algor.com... 

With computers the finite element analysis (FEA) method has greatly enhanced the capability of the structural analyst to calculate displacement, strain, and stress values in complicated plastic structures subjected to arbitrary loading conditions. Details on FEA are reviewed in Chapter 2, Finite Element Analysis. 

There are of course products whose shapes do not approximate a simple standard form or where more detailed analysis is required, such as a hole, boss, or attachment point in a section of a product. With such shapes the component s geometry complicates the design analysis for plastics, glass, metal, or other material and may make it necessary to carry out a direct analysis, possibly using finite element analysis (FEA) followed with prototype testing. Examples of design concepts are presented. 

Algor Finite Element Analysis and other training through Live Webcasts. For webcast schedules see website page http //www.algor.com/webcast/training.htm... 

Savi Ranch Pkwy Yorba Linda, CA 92887 General Inquiries Email info ca.reiusa.com Ftp Site ftp.reiusa.com Phone (714) 974-2500 Fax (714) 974-4771 http //www.reiworld.com/ http //www.reiusa.com/sdyn/sdynO.htm As the world s first commercially available Finite Element Analysis software, STARDYNE has been at the forefront of technology since 1967. Its comprehensive array of Finite Element capabilities allows the engineer to perform in a wide variety of fields—from space vehicles to missiles to nuclear power plants to sophisticated ma-... 

---