The goal of this paper is to obtain an extension of the relaxed saintvenant principle in order to cover the thermoelasticity of dipolar porous. Article information, pdf download for saintvenant end effects in composites. Saintvenants principle and its connections to topology. An analysis of saintvenants principle, in the context for which it was originally intended, is also presented. For example, when solving problems involving bending or axial deformation of slender beams and rods, one does not prescribe loads in any detail. Rationalized and rational jianzhong zhao geophysics department college of resource, environment and earth sciences yunnan university kunming, yunnan, china this is the abstract. Saint venant and navierstokes models for tsunami simulations. Recent developments concerning saintvenant s principle article pdf available in advances in applied mechanics 23 december 1983 with 1,376 reads how we measure reads. The shallow water equations are a set of hyperbolic partial differential equations or parabolic if viscous shear is considered that describe the flow below a pressure surface in a fluid sometimes, but not necessarily, a free surface. Venants principle, the stress will be concentrated near the point of application of load. The saintvenant principle that characterizes such solutions expresses the orthogonality to the interior large wavelength solutions. 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.
I am doing a finite element model of the piers and am making use of st. On the interaction problem between a compressible fluid and a saintvenant kirchhoff elastic structure boulakia, m. Invoking the saintvenant principle, the exact end tractions can be replaced by a statically equivalent system, and this is taken as a uniform loading over the end section. Invoking the saint venant principle, the exact end tractions can be replaced by a statically equivalent system, and this is taken as a uniform loading over the end section. If you like, in a couple of weeks i can share some of the results. Saint venants principle is often invoked to justify approximate solutions to boundary value problems in linear elasticity. Saintvenants principle is a wellknown result in solid mechanics. Pdf on jan 1, 2014, ioneldumitrel ghiba and others published saintvenants principle find, read and cite all the research you need on researchgate.
Saintvenants principle saintvenant was a strong proponent of coordinating experimental and practical work with theoretical study. The approach is designed to be applicable to general nanotubes that can be for instance carbon nanotubes or dna. A variant of the extended formulation of the saintvenant principle is formulated, including its generalization to kinematic parameters. A principle of saintvenant type is established for the theory of linear micropolar elastodynamics, and the connection that exists between this principle and the domain of influence theorems, uniqueness theorems, and continuous dependence theorems is discussed. This estimate can be derived for a large class of potentials including lennardjones potential, when the perfect nanotubes at the equilibrium are stable. Saintvenants 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.
Sirik physicaltechnical group dobroljubova street 2, 29, pavlograd, dnepropetrovsk region, 51400, ukraine the modern form of the saintvenant. 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. With this objective, boussinesq 2 considered received january 5, 1953. Definition of the effects through numerical modelling principia has been working on the development and qualification of two inhouse cfd softwares. The principle says that several characteristic dimensions away from an. Saintvenant principle for kinematic boundary conditions. Saintvenants principle is used to describe the behavior of loads and stresses in an axially loaded member, and may be a factor when considering loads placed upon corroded structures. The saintvenants principle allows elasticians to replace complicated stress distributions or weak boundary conditions with ones that are easier to solve, as long as that boundary is geometrically short. If improving the mesh quality still produces error, we need to check the fidelity of the fe code, if it was not done prior to using the software. In this article we analyze saintvenant end effects for materials with negative poissons ratio.
The statements in different books vary only slightly. It is further assumed that the extensional loading p z is applied at the centroid of the crosssection r so as not to produce any bending effects. I am presently working on distributing some high seismic brace forces to the spillway piers of a dam. We note that the stress field in a composite material can be resolved into two kinds. Consider first the case of an axial resultant end loading p p z e 3 and m 0. Using the lira cad software package, a numerical experiment is carried out, during which the zones of tangential stress disturbances in the support zone of a rigidly clamped ibeam under various kinematic boundary conditions are determined. It states that, when one applies forces on a small region of a body, the local distribution of the forces has little e. Saintvenants principle is important in the application of elasticity solutions in many practical situations in which. This is used very frequently in engineering modelling.
The principle of the elastic equivalence of statically equivalent systems of load, or saintvenants principle, is given a precise mathematical formulation and proof. His greatest contribution to engineering is his approach to modeling practical problems. Journal of composite materials michigan state university. Saintvenants principle and end effects in anisotropic elasticity. Numerical simulation of flow and suspended sediment transport in the distributary channel networks zhang, wei, jia, qiong, and chen, xiaowen, journal of applied.
According to saintvenants principle, when testing structuralsized samples the. Counterexamples to traditional verbal statements of the principle are given, and the results are compared with previous mathematical work on the saintvenant principle. Describe a principle that we call saintvenants principle, and then to employ those stress concentration factors to calculate maximum stresses at discontinuities in structural and machine elements. Saint venants principle as previously mentioned, we generally assume the normal stress distribution in an axially loaded member is uniform, except near the vicinity of the applied load. On the other hand, if the loads on the shell are purely surface loads, then the conclusions concerning the orders of magnitude of the displacements and stresses are the same as those of. Thus, at distances greater than the maximum linear dimensions of the region of load application, the. Moreover, that this is what boussinesq had in mind is apparent from his efforts to justify the principle. This research uses a discretization, for the equations that governs the propagation of a flood wave, in natural rivers, with the objective of a. Aspects of saintvenants principle in the dynamical. Saintvenants principle and stress concentration me. For example, when we solve problems involving bending or axial deformation of slender beams and rods in elementary strength of materials courses, we do not prescribe loads in any detail. Venants principle in justifying a partial model of the dam that only encompasses the spillway piers. Fem method for the eeg forward problem and improvement based on modification of the saint venants method. A reciprocity theorem in linear gradient elasticity and the corresponding saintvenant principle a.
Saintvenant end effects for materials with negative. Instead, the resultant forces acting on the ends of a. Venant s principle, the stress will be concentrated near the point of application of load. Saintvenants principle in linear piezoelectricity semantic scholar. Components used in any system are subjected to various actual or probable forces. The principle of the elastic equivalence of statically equivalent systems of load, or saintvenants principle, is given a precise mathematical formula. And so, for axially loaded beams, we had assumed that there was average uniform stress over.
Venants principle 1 in the mathematical theory of elasticity are well known. Horgan college of engineering michigan state university east lansing, michigan 48824 abstract 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. The stress field remains unchanged in areas of the body which are relatively distant from. Quite analogous to the electrostatics, where the electric field due to the i th moment of the load with 0th being the net charge, 1st the. Saint venant principle an overview sciencedirect topics. A reciprocity theorem in linear gradient elasticity and. Pdf on saintvenants principle in the twodimensional flexural. Saint venant principle concept using on fea duration. Many of the results included have not appeared or been previously discussed in the literature, and illustrative applications are presented throughout. Yang, in basic finite element method as applied to injury biomechanics, 2018. The saintvenant principle states that the effects of loading with the same magnitude but different distributions dissipate quickly as distance increases. Saintvenant principle an overview sciencedirect topics. On saintvenants principle in elasticity sciencedirect. In other words, as the distance from the point of loading becomes greater, the local effects are reduced such.
On saintvenants principle in linear elastodynamics. In doing so, we have unknowingly been applying saint. Saint venants principle article about saint venants. This approach is based on the saint venants principle 5,10,12, which is originally applied in the elasticitys theory. Pdf recent developments concerning saintvenants principle. Mechanics of materialslecture06asaint venants principle duration. Knowles, on saintvenants principle in the twodimensional linear theory of elasticity. Concepts of stress and strain university of arizona. In this blog post, we will explore saintvenants principle, particularly in the context of finite element fe analysis. Saintvenant principle in the theory of elasticity, a principle stating that a system of forces in equilibrium applied to some segment of a solid body produces stresses in that body that rapidly diminish with increasing distance from the segment.
It can be the atmospheric pressure that acts on the fuselage of an. Pdf saintvenants principle and end effects in anisotropic elasticity. Saint venant 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. On a generalized relaxed saintvenant principle boundary value. Solution of saint venants equation to study flood in.
Introduction the classical germainkirchhoff theory of thin elastic plates is known to be the leading term of an interior or outer asymptotic expunsion in. Into the frame of the french tandem project tsunamis in the atlantic and the english channel. Although the average stress along the uniform cross section remains constant, at the point of application of load, the stress is distributed as shown in fig. The intuitive meaning of saint venants 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. Top and bottom plates are rigid and do not rotate 2. Statement of boussinesq or love is ambiguous so that its. Since, in applying the procedure, the effects s are determined it is in principle possible to make the indicated comparison. 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. The problem of statement of saintvenants principle is concerned. Aravas b a department of civil engineering, university of thessaly, volos 38336, greece b department of mechanical and industrial engineering, university of thessaly, volos 38336, greece received 27 august 2004. In this article we consider stress fields which are relevant to saintvenants principle. Numbers in brackets refer to the bibliography at the end of this paper.
1394 938 388 634 725 995 521 872 1224 398 1185 189 623 1408 433 1512 303 1627 1275 603 1064 799 1045 1287 504 214 1012 1162