Pdf the purpose of this paper is to draw attention to the fact that the routine application of saintvenants principle in the solution of elasticity. The principle that the strains that result from application, to a small part of a body s surface, of a system of forces that are statically equivalent to. Saintvenants principle for antiplane shear deformations of. Saintvenants principle and stress concentrations in applying the equations for axial loading of members, we have assumed up to this point that we are sufficiently far enough from the point of load application that the distribution of normal stress is uniform. Experimental problems, whose saint venants principle is established in virtue of supporting experiment, and analytical. The saintvenant principle states that the effects of loading with the same magnitude but different distributions dissipate quickly as distance increases. The intuitive meaning of saint venant s principle is that if two different sets of applied loads are statically equivalent, then the differences between the two stress patterns they create are only significant close to where the loads are applied. Saintvenants principle and end effects in anisotropic elasticity. The saint venant principle states that the effects of loading with the same magnitude but different distributions dissipate quickly as distance increases. Find out information about saint venant s principle. Saintvenant end effects in piezoceramic materials request pdf.
We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. With this objective, boussinesq 2 considered received january 5, 1953. Statement of boussinesq or love is ambiguous so that its. Saintvenant s principle states that if the forces acting on a small portion of an elastic body are replaced by a statically equivalent system of forces on the same portion of the surface, the effect upon the stresses in the body is negligible except in the immediate area affected by the applied forces. Saint venants principle simply states that the stress measured at any point on an axially loaded cross section is uniform given that the measured location is far enough away from the point of load application or any discontinuity in the members cross section. Therefore, the saint venant principle establishes the local nature of the effect of selfequilibrated external loads. I am presently working on distributing some high seismic brace forces to the spillway piers of a dam. Saintvenants principle and stress concentration me. Venant s theory of torsionflexure is restricted to linearbehavior. Venants principle in justifying a partial model of the dam that only encompasses the spillway piers. This paper is concerned with further investigation of the effect of mechanicalelectrical coupling on the decay of saint venant end effects in linear piezoelectricity. Saintvenant principle an overview sciencedirect topics.
It is convenient to express these boundary conditions in terms of stresses in the rod. In this paper, we demonstrate that the neglect of elastic end effects, usually justified by appealing to saint venant s principle, cannot be applied routine ly in problems involving composite mater. Saint venants principle saint venants principle saintvenant did extensive research in the theory of elasticity, and many times he relied on the assumption that local effects of loading do not af fect global strains e. It can be the atmospheric pressure that acts on the fuselage of an aeroplane, or the tension that acts on the cable of a suspension bridge or any other application where a form of force acts on the system. In this paper, we demonstrate that the neglect of elastic end effects, usually justified by appealing to saintvenants principle, cannot be applied routine ly in problems involving composite materials. Components used in any system are subjected to various actual or probable forces. Saint venant end effects in antiplane shear for functionally graded linearly elastic materials c. Toupin s version of the saint venant principle in linear elasticity is generalized to the case of linear elasticity with microstructure. Received july 15, 1972 abstract methods involving energydecay inequalities are applied in investigating saint venant s principle for the plan. Saintvenant end effects for materials with negative. Jun 19, 2018 saint venants principle states that if the forces acting on a small portion of an elastic body are replaced by a statically equivalent system of forces on the same portion of the surface, the effect upon the stresses in the body is negligible except in the immediate area affected by the applied forces.
Closure to discussion of vibration of a group of circular cylinders in a confined fluid 1978, asme j. Stiff face layers if the face layers are much stiffer than the core, but not perfectly rigid, new roots appear for the eigenvalue equation which were not anticipated in the above case choi and horgan, 1978. Mises the socalled principle of statically equivalent loads, due to saint venant, has been referred to for the last fifty years in almost all texts on elasticity. That is, it is shown that, for a straight prismatic bar made of an isotropic linear elastic material with microstructure and loaded by a selfequilibrated force system at one end only, the strain energy stored in the portion of the bar which is beyond a. Saintvenant end effects in antiplane shear for functionally. Saint venants principle and stress concentrations in applying the equations for axial loading of members, we have assumed up to this point that we are sufficiently far enough from the point of load application that the distribution of normal stress is uniform. We note that the stress field in a composite material can be resolved into two kinds. The solution is not unique, but saint venants principle guarantees that all the solutions will approach one another away from the ends of the rod. Thus, at distances greater than the maximum linear dimensions of the region of load application, the stresses and deformations are negligibly small. On saint venant s principle in plane anisotropic elasticity cornelius o. Using classical elasticity theory, horgan 14 has investigated the decay of end effects in anisotropic materials and has concluded that the end effects decay slowly in highly anisotropic materials.
The problem of statement of saint venants principle is concerned. Counterexamples to traditional verbal statements of the principle are given, and the results are compared with previous mathematical work on the saint venant principle. Topic 3 fundamental principles massachusetts institute of. Dec 30, 2015 blended learning video for the mechanics of materials course offered by the faculty of aerospace engineering at delft university of technology.
In this blog post, we will explore saintvenants principle, particularly in the context of finite element fe analysis. The statements in different books vary only slightly. Beginning with the simplest case of saint venants principle, four problems of elasticity are discussed mathematically. Numerical simulation of flow and suspended sediment transport in the distributary channel networks zhang, wei, jia, qiong, and chen, xiaowen, journal of applied. It is concluded that there exist two categories of elastic problems concerning saint venants principle. Decaying states in a plate of general shape i007 in 10, the authors developed the notion of a decaying state for the particular case of the semiinfinite plate x 2 0, 1 y 1 c 1m, 1z 5 15, which was tractionfree on z h and subject to plane strain deformation independent of y. Saintvenant end effects in antiplane shear for functionally graded linearly elastic materials c. The respective strain values obtained from both the gages are measured and then plotted with respect to time. On saintvenants principle in plane anisotropic elasticity. Toupin s version of saint venant s principle in linear elasticity is generalized to the case of linear piezoelectricity. Saintvenant solutions saint venants principle end effects transition effects delamination composites abstract we present a rigorous veri. Blended learning video for the mechanics of materials course offered by the faculty of aerospace engineering at delft university of technology.
If you like, in a couple of weeks i can share some of the results. I am doing a finite element model of the piers and am making use of st. Yang, in basic finite element method as applied to injury biomechanics, 2018. The stress field remains unchanged in areas of the body which are relatively distant from the surfaces upon which the forces are changed.
End effects may be particularly pronounced when such materials attain extreme limits on poisson s ratio or on nonlocal behavior, or if they have rigid elements connected by hinges. This paper is concerned with investigation of the effect of mechanicalelectrical coupling on the decay of saint venant end effects in linear piezoelectricity. Venant 1855 proposed this principle on the basis of his analyses of end effects in slender elastic beams and shafts. On the interaction problem between a compressible fluid and a saint venant kirchhoff elastic structure boulakia, m. Use of negative poissons ratio foam as core is possible. That is, it is shown that, for a straight prismatic bar made of a linear piezoelectric material and loaded by a selfequilibrated system at one end only, the internal energy stored in the. The utm is then switched on and the specimen subjected to tensile load. Abstract in this article we analyze saint venant end effects for materials with negative poisson s ratio. Saint venants principle and end effects in anisotropic elasticity a commentary has been published. Moreover, that this is what boussinesq had in mind is apparent from his efforts to justify the principle. Saint venants principle article about saint venants. Venants principle, the stress will be concentrated near the point of application of load. Saintvenant s principle tells us that the exact distribution of a load is not important far away from the loaded region, as long as the resultants of the load are correct. The purpose of this paper is to draw attention to the fact that the routine application of saintvenants principle in the solution of elasticity problems involving highly anisotropic or composite materials is not justified in general.
It is an exact linear formulation for a prismatic member subjected to a prescribed f the case where the crosssectional shape is constant but the orientation varies along the centroidal axis is treated in chapter 15. Quintanilla mathematics and mechanics of solids 2016 6. Saint venants principle saintvenant did extensive research in the theory of elasticity, and many times he relied on the assumption that local effects of loading do not affect global strains e. Rationalized and rational jianzhong zhao geophysics department college of resource, environment and earth sciences yunnan university kunming, yunnan, china this is the abstract. In doing so, we have unknowingly been applying saint. Numbers in brackets refer to the bibliography at the end of this paper. A study of saintvenants principle for composite materials. Horgan 2 department of engineering mechanics, the university of michigan, ann arbor, michigan. Saintvenant principle article about saintvenant principle. In other words, as the distance from the point of loading becomes greater, the local effects are reduced such that they can be considered not to be present.
Saintvenant end effects for materials with negative poisson. Saint venant s principle and related results for elasticity theory have received considerable attention in the literature but relatively little is known about analogous issues in piezoelectricity. Pdf saintvenants principle and end effects in anisotropic. This is used very frequently in engineering modelling.
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