Finite-element analysis techniques

ERF are in the process of evaluating stress variations of panels under given loading conditions using finite element analysis techniques. 

The finite element analysis technique has been used very successfully to confirm the regions of concentrated stress and strain. In this technique, the bonded assembly is subdivided into small elements and the forces relevant to each element are computed using basic mathematical equations. This is very useful, particularly in the understanding of complex joint designs. 

In 1973, Hart-Smith took this a stage further by considering the plastic deformation of an adhesive in addition to the elastic response. This work, coupled with the finite element analysis technique provided the platform for calculation of stress distribution in complex nonlinear joints. The finite element approach to stress analysis is very convenient because the number of elements can be increased in areas of significant stress change. 

Fig. 10-15. The 2-D bracket was optimized using iterative finite element analysis techniques. The General Motors Research Laboratories.)...

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

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. 

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. 

AI methods may be used in various ways. The models may be used as a standalone application, e.g., in recent work on the design of microwave absorbers using particle swarm optimization (PSO).6 Alternatively, a computational tool, such as a finite element analysis or a quantum mechanical calculation, may be combined with an AI technique, such as an evolutionary algorithm. 

In particular, the techniques based on the termination of certain plies within the laminate has also shown promise. Static tensile tests of [30°/-30°/30°/90°]s carbon-epoxy laminates containing terminals of [90°] layers at the mid-plane show that premature delamination is completely suppressed with a remarkable 20% improvement in tensile strength, compared to those without a ply terminal. Cyclic fatigue on the same laminates confirms similar results in that the laminate without a ply terminal has delamination equivalent to about 40% of the laminate width after 2x10 cycles, whereas the laminates with a ply terminal exhibit no evidence of delamination even after 9x10 cycles. All these observations are in agreement with the substantially lower interlaminar normal and shear stresses for the latter laminates, as calculated from finite element analysis. A combination of the adhesive interleaf and the tapered layer end has also been explored by Llanos and Vizzini, (1992). 

The main interest in finite element analysis from a testing point of view is that it requires the input of test data. The rise in the use of finite element techniques in recent years is the reason for the greatly increased demand for stress strain data presented in terms of relationships such as the Mooney-Rivlin equation given in Section 1 above. 

Prior to any production for complex and critical applications, theoretical calculations should be carried out to assess the properties of the selected grade. Computerized mathematical techniques such as finite element analysis can be carried out to determine potential stress points. There are also mold-filling programs that can be used. Both these methods are expensive and need specialized staff. 

The failure analysis can be done using a judicious combination of several methods such as visual examination, metallography, microscopy, electron microprobe, energy dispersive X-ray analysis, X-ray diffraction methods for determining residual stress in the sample, surface analytical techniques to determine the nature and composition of surface deposits and finite element analysis modeling. 

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. 

For the coarse estimation of extruder size and screw speed, simple mass and energy balances based on a fixed output rate can be used. For the more detailed design of a twin-screw extruder configuration it is necessary to combine implicit experience knowledge with simulation techniques. Theses simulation techniques cover a broad range from specialized programs based on very simple models up to detailed Computational Fluid Dynamics (CFD) driven by Finite Element Analysis (FEA) or Boundary Element Method (BEM). 

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. 

The methods developed in this book can also provide input parameters for calculations using techniques such as mean field theory and mesoscale simulations to predict the morphologies of multiphase materials (Chapter 19), and to calculations based on composite theory to predict the thermoelastic and transport properties of such materials in terms of material properties and phase morphology (Chapter 20). Material properties calculated by the correlations presented in this book can also be used as input parameters in computationally-intensive continuum mechanical simulations (for example, by finite element analysis) for the properties of composite materials and/or of finished parts with diverse sizes, shapes and configurations. The work presented in this book therefore constitutes a "bridge" from the molecular structure and fundamental material properties to the performance of finished parts. 

That means that for a produced Ao, the cantilever bending will be higher for longer and thinner cantilevers, i.e., with low stiffness. The parameter that characterizes the cantilever stiffness is the spring constant, which depends on the cantilever dimensions and Young s modulus (see Subheading 3.2). The biomolecular interactions could be difficult to detect with commercial micro-cantilevers due to the low surface stress induced on such micro-cantilevers. To improve the cantilever deflection, this parameter, and its dimensions dependency, needs to be simulated before fabrication. The simulation was performed using a finite element analysis (FEA) technique (with ANSYS software). 

Robust validation data for residual-stress models require experimentally intensive and costly diffraction testing, using neutrons or x-rays. The particular value of synchrotron x-ray techniques has been illustrated for several aluminum welding studies, including FSW applied to dissimilar alloys (Ref 88-90). Bringing together the finite element analysis of residual stress and the extensive synchrotron data is a matter of current research. 

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