Deflection (engineering)

Summary

In structural engineering, deflection is the degree to which a part of a structural element is displaced under a load (because it deforms). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations. Otherwise methods such as virtual work, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method are used. The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications. Beam deflection for various loa

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Analysis of the deflection of a circular membrane under differential pressure (bulge test) is a well-known method of determining the elastic properties of thin films. However, analytical models always suffer from simplifying hypotheses. In this study we present a new approach, based on numerical modeling, to interpret pressure-deflection curves. By adjusting Young’s modulus and Poisson’s ratio in the simulation program, it is possible to reproduce the experimental curves faithfully. The method was successfully tested with two different materials (silicon and aluminium) with known elastic properties and was then used to determine biaxial Young’s moduli of CVD diamond thin films for three different microstructures. The values of E varied from 565 to 620 GPa (assuming a Poisson ratio of 0.1). Grain boundaries are thought to be responsible for the relatively low values of Young’s moduli. Uncertainties in E are relatively large (lo%-15%) because the method is highly sensitive to experimental parameters such as thickness or membrane diameter and to the initial residual stress state which is known only approximately.

Elsevier1996

The effects of the post-yield behaviour on the shape of small ball punch test (SBPT) curves were investigated with finite element simulations from which the load-deflection curves were extracted. We have shown the general yield load defined on the ball punch curves depends on the post-yield behaviour and that the usual linear calibration between the yield load and the yield stress may lead to erroneous estimations of the irradiation-hardening. A new calibration procedure has been proposed to determine the yield stress from a ball punch curve that makes use of empirical parameters that minimizes the effects of the post-yield behaviour which influence the overall shape of the ball punch test from the very beginning of the tests.

Elsevier2009

We present an assessment of the mechanical constitutive behavior after irradiation for a tempered martensitic steel, Eurofer97', and for Zircaloy by means of small-ball punch tests. For that purpose we use a finite-element model of the punch test device. We take advantage of the model to infer the alloy mechanical constitutive behavior after irradiation. We show that a necessary matching between the experimental and calculated force-deflection curves allows choosing consistently among the proposed constitutive behaviors. We discuss also the limitations of this method. For Zircaloy a complete description of the constitutive behavior in the unirradiated or irradiated condition was not possible in the framework of anisotropic plastic potentials and associated flow rules, since this demands to fully characterize experimentally the anisotropic yield surface and its evolution with plastic strain during punch deformation. However, an approximate description of the initial yielding anisotropy using Hill plastic potential is possible (although not unique) and necessary before an assessment of the irradiation- hardening can be done on a safe basis. Developing a conventional (non-axisymmetric) three-dimensional model was mandatory in order to deal with the problem of anisotropy in Zircaloy. (c) 2005 Elsevier B.V. All rights reserved.

2005