Advanced finite element techniques

When required, combined with the use of computers, the finite element analysis (FEA) method can greatly enhanced the capability of the structural analyst to calculate displacement and stress-strain values in complicated structures subjected to arbitrary loading conditions. In its fundamental form, the FEA technique is limited to static, linear elastic analysis. However, there are advanced FEA computer programs that can treat highly nonlinear dynamic problems efficiently. 

Over the past few years, however, techniques have been developed to enable continuous reinforcement of thermoplastics. The simplest way is to put a cloth and a plastic sheet on top of each other in a heated press and to carry out impregnation under pressure. More difficult is the forming of an end-product from the sheet produced with conventional sheet-forming techniques the position of the fibres will be distorted in an unacceptable way. As in nearly all processing techniques, the modern finite-element methods with advanced computers are able to present solutions to this problem in principle they can predict the position of the fibres in the sheet-forming operation, so that optimum reinforcement is realised in the end product. 

In this limited space, it is not possible to provide an exhaustive survey of the advanced techniques for simulations, for which see Ref [2], especially the 3rd edition. Here, only those advances that have helped to overcome the major problems of thin reaction layers, coupled systems, and efficiency, will be mentioned. Such excellent methods as orthogonal collocation, finite elements, or other sophisticated methods are left out of necessity. 

Recent theoretical studies have become much more complex. New computer-assisted techniques permit the use of finite-element matrix-theory type approaches. The effects of important variables are being determined by parametric studies. More complex joints are also being studied. New adherend materials, including advanced filamentary composites, are also being evaluated. The elastic, low-deflection, constant temperature behavior of scarf and stepped-lap joints has been replaced by elastic-plastic, large-deflection behavior, combined with thermal expansion differences, or curing shrinkage-induced residual stresses. 

Expressions for the limiting shape factors when the width of the channel is small relative to the depth (W H ) are given hy Booy [29]. However, this type of channel geometry is generally not encountered in commercial twin screw systems. Numerical simulation of the flow and heat transfer in twin screw extruders is covered in Chapter 12. Section 12.3.2 discusses 2-D analysis of twin screws, and Section 12.4.3.3 deals with 3-D analysis of flow and heat transfer in twin screw extruders. Since 2000, major advances have been made in the numerical methods used to simulate twin screw extruders. The boundary element method now allows full 3-D analysis of flow in TSEs. A significant advance in the finite element method is the mesh superposition technique that allows analysis of complicated geometries with relative ease. This is discussed in more detail in Chapter 12. 

The first model proposed for approximated analysis of the left ventricle of the heart was a spherical shell (Pao, 1980a and Mirsky, 1974) which was adopted by Woods in 1892 so that the Laplace law could be applied for calculation of the wall stresses. When the biplane silhouettes can be obtained by the X-ray technique, the left ventricle has since been analyzed as axisymmetric thick-walled shells. The advances in computer-aided tomography in recent years make it possible to image and reconstruct the cross-sectional shapes of the heart (Ritman, 1983). As a result of this development, the true three-dimensional structural shape of the heart can be accurately formed by stacking of the reconstructed cross sections together. Various finite element models have been proposed (Figure 1) for the analyses of the ventricles as well as for the cardiac valves both natural and prothetic (Pao,... 

In certain zones such as embedded items areas would create where stresses in concrete are unacceptable reinforcement may be arranged to reduce these stresses. Due to temperature hot spots may occur in concrete zones which could be unacceptable. The stresses could be high. By providing some of these local reinforcement will reduce stresses to acceptable values in concrete. The most appropriate technique is to use advance analytical means such as finite element. Stress trajectories with and without reinforcement could be developed. These stress trajectories would determine the sizes and the zones to which these reinforcement could form shapes. The extent of such reinforcement will have bond lengths between 24 and 48 diameters of the bar. Obviously these reinforcement would be evaluated under prestressing anchorages too to avoid cracks under stressing loads. 

An important step in local strain fatigue analysis under irregular variation of load with time, as schematized in Fig. 6.16a, is the knowledge of the local notch strain-stress history, as shown in Fig. 6.16c. This, in turn, necessitates the knowledge of the cyclic stress-strain characteristic of the material (see Sect. 1.3.1). Advanced elastic-plastic analysis technique such as finite element computer code is needed or it can be used a simplified Neuber s rule as described in the next section. 

The described procedure for connecting different substructures implies that the finite element mesh at the interface of the substructures is identical. However, there are more advanced techniques which allow the connection of substructures even when neither mesh pattern nor element types match along the interface (Knight et aL 1991 Zhao et al. 1999 Dohrmann et al. 2000 Gmiir and Kauten 1993). 

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