Finite stress brake disk, electrical analysis of a piezoactuator

Finite element analysis is a computerized method usedin manufacturing processesto analyze, optimize, predictand control how a material or product reacts to real world forces, vibrations, stresses, heat, fluid flow and other physical effects1. It was first developed in 1943 by R. Courant and has been used traditionally ever since then tosolve solid mechanics problems. It is a very important tool as it can be used to determine the points of weakness in a design before it ismanufactured as well as a predict if a product is likely to wear out, break, or work the way it was designed to. The modern use of Finite element analysisstarted in the field of structural engineering. Itcanalsobe applied nowadays in the modeling and simulation of other engineering systems i.e the dynamics of an earthquake or bullet impact, thermal analysis of a stress brake disk, electrical analysis of a piezoactuator or even the analysis of biomaterials like human organ and tissues. Focusing on Mechanical engineering, FEA has been used in five major topics namely: Fluid mechanism and heat transfer, machine element analysis and design, wave propagation and failure-analysis, machining and product design and structural mechanics and composite materials. There have been a lot of new developments in FEA i.e Integrating FEA into CAD design/Solidworks software (the analysis can be done as you design), self-adaptive analysis (change the mesh during the analysis), Multi-scale analysis (analyzing physical problems ranging from atomistic level to microscopic level and combining FEA with molecular dynamics simulations), Analysis of problem of huge size (analyze a model with millions of nodes; parallel computing) and multi-physics analysis (Mechano-electrical coupling(MEMS); Mechano-chemical coupling(Chemical-mechanical polishing(CMP))In this paper I will be focusing on the use of FEA in analyzing fluid mechanism, thermal analysis/heat transferin comparison to structural analysis. From my experience taking fluid mechanics and heat transfer, practical engineering problems in these courses usually require one or more fundamental equations, together with a boundary condition over a complex/non-uniform domain3. And this is where finite element method becomes a powerful tool to numerically analyze problems in these areas. In fluid flow, heat transfer, and mass transfer, FEA analysis are based on the laws of conservation of momentum, mass, and energy. The flues in these conservation laws are typically composed of advection and dissipation or diffusion. The main idea of the FEM is to discretize this complex domain into several subdomains, or finite elements. In terms of heat transfer and thermal analysis, FEA methods could be used in conjunction with a structural FEA analysis3. And this extension from a structural FEA solution to thermal FEA solution can only be done because there are direct analogies between the variables we are solving for i.e the stiffness (in the matrices) becomes thermal conductivity, displacements become temperatures, the stress is the heat flux and the load is the heat. In many cases, the thermal analysis objective is to provide the temperature distribution for subsequent stress analysis. A steady-state temperature distribution is mapped from thermal model to thestructural model in a typical uncoupled thermal and structural solution. Mapping can be direct within the same physical mesh, or interpolated between dissimilar mesh models. Either approach will result in thermal strains throughout the structure. If componentsuch as a bar is allowed to freelyexpand under a uniform soak of temperature change then it will have a constant thermal strain throughout and no induced stresses. However, if both ends of the bar are held, then the thermal strains are opposed by induced mechanical strains(the bar will not expand naturally). In practice, components will have a more complex temperature distribution of thermal properties as well as mechanical boundary condition and will develop thermal stresses throughout, even if nominally free to expand.A very good example of this is a bimetallic strip.This figure above shows the analysis of a nonlinear structure with thermal loading using FEA. The bar is free to expand in a stress free manner until a small gap is taken up with an adjacent block. At this point, the stresses will increase from zero. An initial thermal analysis is not needed in this case because the temperature field is just a constant elevated temperature, whichis defined as a thermal loading in a structural sense directly into the stress analysis. However as the gap is closing a nonlinear static solution is required. Just as in structural analysis using the FEA method, thermal solutions can suffer various inaccuracies as well. The FEA solution is always a discretization of a continuous response. The accuracy of structural analysis is usually accessed by looking at the stress jumps between adjacent elements, and attempting to achieve a convergence. In view of thermal analysis, the temperature distribution is the most commonly presented form of thermal response, typically a contour plot. The figure above shows the thermal singularity in sharp corners using heat flux contour plots2.However, to obtain a better feeling for how accurate the solution is, the heat flux passing through each element should be analyzed (which means the stress in the structural solution and hence is a good indictor of convergence and accuracy). Thermal FEA solutions are relatively straightforward to set up, however obtaining the required accuracy, idealization methods and mesh discretization can be challenging. A smooth temperature contour plot is not a very good indicator; instead the heat flux convergence is a better guide and is analogous to the stress convergence in a structural solution2. The advantages of FEA are numerousi.e the comprehensive result sets, extrapolation of existing experimental via parametric analyses of validated models, the simultaneous calculations and visual presentation of widevariety of physical parameters like temperature or stress, ensuring ease of analyzing performance and possible modifications and relatively low investment and rapid calculation time for this application. The FEA process incorporates many steps and many details such as the choice of numerous parameters, which control the solution process, have been successfully automated and do not need much user attention. FEA is much more streamlined today then the software of the last generation and it’s available to engineers and smaller enterprises at affordable prices5. However, there’s still a lot more to done so that FEA potential can provide better engineering designs that can be fully realized. An important current trend is to lighten the burden of computational method details on the engineers, designers, and researchers who use FEA for their specific application. Both algorithms and user interfaces are continuously being improved. New software interfaces are being developed to help FEA expertsbuild application-specific tools, together with an application expert, which allows the engineer to concentrate on design tasks. I would say the future of the FEA software is looking bright.

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