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. On the interaction problem between a compressible fluid and a saint venant kirchhoff elastic structure boulakia, m. 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. 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. I am presently working on distributing some high seismic brace forces to the spillway piers of a dam. Experimental problems, whose saint venants principle is established in virtue of supporting experiment, and analytical. Closure to discussion of vibration of a group of circular cylinders in a confined fluid 1978, asme j. 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. It is convenient to express these boundary conditions in terms of stresses in the rod. Beginning with the simplest case of saint venants principle, four problems of elasticity are discussed mathematically.
In doing so, we have unknowingly been applying saint. Thus, at distances greater than the maximum linear dimensions of the region of load application, the stresses and deformations are negligibly small. Yang, in basic finite element method as applied to injury biomechanics, 2018. 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. Components used in any system are subjected to various actual or probable forces. 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. In this blog post, we will explore saintvenants principle, particularly in the context of finite element fe analysis. 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. Saint venant end effects in antiplane shear for functionally graded linearly elastic materials c. Saintvenant end effects in antiplane shear for functionally. Therefore, the saint venant principle establishes the local nature of the effect of selfequilibrated external loads. On saint venant s principle in plane anisotropic elasticity cornelius o. Numerical simulation of flow and suspended sediment transport in the distributary channel networks zhang, wei, jia, qiong, and chen, xiaowen, journal of applied. Saintvenant end effects in piezoceramic materials request pdf.
Venants principle, the stress will be concentrated near the point of application of load. 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. Topic 3 fundamental principles massachusetts institute of. 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. Saintvenant end effects for materials with negative. Venant s theory of torsionflexure is restricted to linearbehavior. The saintvenant principle states that the effects of loading with the same magnitude but different distributions dissipate quickly as distance increases. Venants principle in justifying a partial model of the dam that only encompasses the spillway piers. We note that the stress field in a composite material can be resolved into two kinds. 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. 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. Moreover, that this is what boussinesq had in mind is apparent from his efforts to justify the principle.
Blended learning video for the mechanics of materials course offered by the faculty of aerospace engineering at delft university of technology. Dec 30, 2015 blended learning video for the mechanics of materials course offered by the faculty of aerospace engineering at delft university of technology. Statement of boussinesq or love is ambiguous so that its. If you like, in a couple of weeks i can share some of the results. 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. 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. Find out information about saint venant s 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. The utm is then switched on and the specimen subjected to tensile load. Rationalized and rational jianzhong zhao geophysics department college of resource, environment and earth sciences yunnan university kunming, yunnan, china this is the abstract.
Saintvenant principle an overview sciencedirect topics. 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. The stress field remains unchanged in areas of the body which are relatively distant from the surfaces upon which the forces are changed. The problem of statement of saint venants principle is concerned. Saintvenant end effects for materials with negative poisson. Saint venants principle and end effects in anisotropic elasticity a commentary has been published. Toupin s version of saint venant s principle in linear elasticity is generalized to the case of linear piezoelectricity.
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. 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. Received july 15, 1972 abstract methods involving energydecay inequalities are applied in investigating saint venant s principle for the plan. 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.
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. Saint venants principle article about saint venants. 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. Saintvenant end effects in antiplane shear for functionally graded linearly elastic materials c. Abstract in this article we analyze saint venant end effects for materials with negative poisson s ratio. Saintvenant principle article about saintvenant principle.
It is concluded that there exist two categories of elastic problems concerning saint venants principle. 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. 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. Numbers in brackets refer to the bibliography at the end of this paper. The respective strain values obtained from both the gages are measured and then plotted with respect to time. This is used very frequently in engineering modelling. 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. The principle of the elastic equivalence of statically equivalent systems of load, or saint venant s principle, is given a precise mathematical formulation and proof. Saintvenants principle and stress concentration me. This paper is concerned with further investigation of the effect of mechanicalelectrical coupling on the decay of saint venant end effects in linear piezoelectricity. Saintvenants principle and end effects in anisotropic elasticity. Pdf saintvenants principle and end effects in anisotropic.
On saintvenants principle in plane anisotropic elasticity. The statements in different books vary only slightly. 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. A study of saintvenants principle for composite materials. Use of negative poissons ratio foam as core is possible. 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. Toupin s version of the saint venant principle in linear elasticity is generalized to the case of linear elasticity with microstructure. Horgan 2 department of engineering mechanics, the university of michigan, ann arbor, michigan. Venant 1855 proposed this principle on the basis of his analyses of end effects in slender elastic beams and shafts. I am doing a finite element model of the piers and am making use of st.
Quintanilla mathematics and mechanics of solids 2016 6. With this objective, boussinesq 2 considered received january 5, 1953. 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. Saintvenants principle for antiplane shear deformations of.