Elastic Element Methods

Elastic-Element Methods Elastic-element pressure-measuring devices are those in which the measured pressure deforms some elastic material (usually metallic) within its elastic limit, the magnitude of the deformation being approximately proportional to the applied pressure. These devices may be loosely classified into three types Bourdon tube, bellows, and diaphragm. 

Barometry measures a broad variety of pressures using an equally broad variety of measurement techniques, including liquid column methods, elastic element methods, and electrical sensors. Electrical sensors include resistance strain gauges, capacitances, piezoresistive instruments, and piezoelectric devices. The technologies range from those developed by French mathematician Blaise Pascal, Greek mathematician Archimedes, and Torricelli to early twenty-first century MEMS sensors and those used to conduct nanoscale materials science. 

Vol. 8. Contact Problems in Elasticity A Study of Variational Inequalities and Finite Element Methods N. Kikuchi and J. T. Oden... 

The finite-element method applied in the elastic-plastic mode gives satisfactory predictions of the achievable improvements from autofrettage. As the residual stresses reduce efficiently the initiation and the growth of cracks, autofrettage is especially well useful for components... 

A finite element method is employed to study the nonlinear dynamic effect of a strong wind gust on a cooling tower. Geometric nonlinearities associated with finite deformations of the structure are considered but the material is assumed to remain elastic. Load is applied in small increments and the equation of motion is solved by a step-by-step integration technique. It has been found that the cooling tower will collapse under a wind gust of maximum pressure 1.2 psi. 13 refs, cited. 

The calculation of thermal stresses in functionally graded materials is already a relatively old topic (Yang et al., 2003). Two methods can be distinguished analytical methods and finite element methods. However, the complicating effect of the elastic modulus variation with the position severely limits the scope of problems that can be solved analytically. Therefore, the majority of the analytical work has been for FGM films or other simple structures (Becker et al., 2000). Analytical models have been developed for the calculation of thermal stresses for 1-D FGM symmetrical plates (Jung et al., 2003), non-... 

J. T. Oden and T. Sato, Finite Strains and Displacements of Elastic Membranes by the Finite Element Method, Int. J. Solids and Struct., 3, 471 -88 (1967). 

G. Harkegard Application of the finite element method to cyclic loading of elastic-plastic structures containing effects. Int. J. Fract. 9, 322 (1973)... 

In the following results are presented for the application of the Boundary Finite Element Method both for the case of the laminate free-edge effect and for the case of a single transverse matrix crack in the framework of linear elasticity theory. 

From the standpoint of the continuum simulation of processes in the mechanics of materials, modeling ultimately boils down to the solution of boundary value problems. What this means in particular is the search for solutions of the equations of continuum dynamics in conjunction with some constitutive model and boundary conditions of relevance to the problem at hand. In this section after setting down some of the key theoretical tools used in continuum modeling, we set ourselves the task of striking a balance between the analytic and numerical tools that have been set forth for solving boundary value problems. In particular, we will examine Green function techniques in the setting of linear elasticity as well as the use of the finite element method as the basis for numerical solutions. 

Recall from chap. 2 that often in the solution of differential equations, useful strategies are constructed on the basis of the weak form of the governing equation of interest in which a differential equation is replaced by an integral statement of the same governing principle. In the previous chapter, we described the finite element method, with special reference to the theory of linear elasticity, and we showed how a weak statement of the equilibrium equations could be constructed. In the present section, we wish to exploit such thinking within the context of the Schrodinger equation, with special reference to the problem of the particle in a box considered above and its two-dimensional generalization to the problem of a quantum corral. 

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. 

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