Saintvenant end effects in antiplane shear for functionally. Statement of boussinesq or love is ambiguous so that its. Ppt saint venants principle powerpoint presentation free. 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 saint venant s principle, cannot be applied routine ly in problems involving composite materials. Saintvenants principe of the problem of the cylinder. Since these considerations are related to what is called saint venant s principle we conclude with a discussion of this principle. The principle says that several characteristic dimensions away from an effect, the effect is essentially. Pdf saintvenant end effects for anisotropic materials. The axisymmetrical deformation of the in nite circular cylinder loaded by an equilibrium system of forces on its near end is discussed and its formulation of modi ed saint venants principle is established. Since these considerations are related to what is called saintvenants principle we conclude with a discussion of this principle.
Venants principle for end effects uniqueness theorem % 5 41 2d problems in elasticity plane stress and plane strain problems stress compatibility equation airys stress function and equation polynomial method of solution solution for bending of a cantilever with and end load 4 first internal exam iii. Thus, at distances greater than the maximum linear dimensions of the region of load application, the. Components used in any system are subjected to various actual or probable forces. This paper is concerned with further investigation of the effect of mechanicalelectrical coupling on the decay of saint venant end effects in linear piezoelectricity. Toupins version of the saintvenant principle in linear elasticity is generalized to the case of linear elasticity with microstructure. Saint venants principle and end effects in anisotropic elasticity. Venants principle, the stress will be concentrated near the point of application of load. By invoking saintvenants principle, one assumes that the effect of self equilibrated loads on an object is purely local, and that stress due to such loads decays rapidly with distance. Venants principle in justifying a partial model of the dam that only encompasses the spillway piers. Toupin s version of the saint venant principle in linear elasticity is generalized to the case of linear elasticity with microstructure. End effects may be particularly pronounced when such materials attain extreme limits on poissons ratio or on nonlocal behavior, or if they have rigid elements connected by hinges. Saintvenants principle and end effects in anisotropic. Saint venants principle article about saint venants. The stress field remains unchanged in areas of the body which are relatively distant from the surfaces upon which the forces are changed.
Saintvenant end effects in antiplane shear for classes. This is used very frequently in engineering modelling. 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. By invoking saint venant s principle, one assumes that the effect of self equilibrated loads on an object is purely local, and that stress due to such loads decays rapidly with distance. A saint venant principle for a theory of nonlinear plane elasticity by c. Quintanilla mathematics and mechanics of solids 2016 6. The principle of saint venant allows us to simplify the solution of many problems by altering the boundary conditions while keeping the systems of applied forces statically equivalent. The saint venant principle permits the substitution of a set of boundary conditions effective forces by another for example, a set more convenient for static calculation under the condition that the resultant and moment of the new system retain the values of the former system. 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 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. On saintvenants principle in plane anisotropic elasticity. Rationalized and rational jianzhong zhao geophysics department college of resource, environment and earth sciences yunnan university kunming, yunnan, china this is the abstract. Venants principle to the class of bimaterial straight edge stress singularity problems, first investigated by pipes and pagano in the special case of a free edge and antiplane shear loading. A study of saint venants principle for composite materials by means of internal stress fields yutaka arimitsu.
Journal of composite materials college of engineering. Horgan and others published saint venant end effects for anisotropic materials find, read and cite all the research you need on researchgate. Pdf saintvenants principle and end effects in anisotropic. 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.
Payne cornell university, ithaca, new york 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. 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. I am presently working on distributing some high seismic brace forces to the spillway piers of a dam. Toupins version of saintvenants principle in linear elasticity is generalized to the case of linear piezoelectricity. The statements in different books vary only slightly. Axial loads, saint venant s principle, displacement duration. We note that the stress field in a composite material can be resolved into two kinds. The stress field remains unchanged in areas of the body which are relatively distant from. On saintvenants principle in plane anisotropic elasticity 171 flp avq ap3 aq3 p, q 1, 2, 6, 2.
Saintvenant principle article about saintvenant principle. 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. Venants theory of torsionflexure is restricted to linearbehavior. Topic 3 fundamental principles free online course materials. The saint venants principle, as enunciated in terms of the strain energy functional, does not.
A satisfactory approximate solution can be obtained. Saintvenants principle and stress concentration me. 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. 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. On the interaction problem between a compressible fluid and a saint venant kirchhoff elastic structure boulakia, m. 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.
A rigorous approach is presented to investigate the applicability of st. Saint venants principle also applies to other slender members. Abstract in this article we analyze saintvenant end effects for materials with negative poissons ratio. A formulation of saintvenants principle within the context of a restricted theory of nonlinear plane elasticity is described. 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 saint venants principle, cannot be applied routine ly in problems involving composite materials. The saintvenant principle states that the effects of loading with the same magnitude but different distributions dissipate quickly as distance increases. Saint venant end effects in antiplane shear for functionally graded linearly elastic materials c. His greatest contribution to engineering is his approach to modeling practical problems. The statement of modi ed saint venants principle is suggested. Horgan university of virginia, charlottesville, virginia and l. A study of saintvenants principle for composite materials.
The purpose of this paper is to draw attention to the fact that the routine application of saint venants principle in the solution of elasticity problems involving highly anisotropic or composite materials is not justified in general. The interior large wavelength effect must be separated from the edge or extremity effects with a small wavelength to be computed. Let an elastic body with lame constants x and v occupy a region d with piecewise smooth boundary i\ in the absence of body. 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. 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 solid mechanics, it is common to analyze the properties of beams with constant cross section. 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. A formulation of saint venant s principle within the context of a restricted theory of nonlinear plane elasticity is described.
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. 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 traction free on z h and subject to plane strain deformation independent of y. In this blog post, we will explore saintvenant s principle, particularly in the context of finite element fe analysis. 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. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1. Venants principle for end effects uniqueness theorem % 5 41 2d problems in elasticity plane stress and plane strain problems stress compatibility equation airys stress function and equation polynomial method of solution solution for bending of a cantilever with and end load 4. This paper is concerned with further investigation of the effect of mechanicalelectrical coupling on the decay of saintvenant end effects in linear piezoelectricity. The saint venant s principle is considered from the angle of its present practical interest in structural mechanics, especially for composite structures. A saintvenant principle for a theory of nonlinear plane elasticity by c. The problem of statement of saint venants principle is concerned. 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. 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. Venant s principle, the stress will be concentrated near the point of application of load. Fem method for the eeg forward problem and improvement based on modification of the saint venants method. Chapter objectives determine deformation of axially loaded members develop a method to find support reactions when it cannot be determined from equilibrium equations analyze the effects of thermal stress, stress concentrations, inelastic deformations, and residual stress 4. Fem method for the eeg forward problem and improvement based on modification of the saint venant s method. Jul 19, 2017 saint venants end effect principle mech ktu lectures. Saintvenants principle and stress concentration me mechanical. 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.
I am doing a finite element model of the piers and am making use of st. Thus on a circle of large radius r the stress in the x direction, on. In linear elasticity, saint venants principle is used to show that selfequilibrated loads generate local stress effects that decay away from the loaded end of a structure. On saintvenants principle in elasticity sciencedirect. It is evident that nding solutions of boundaryvalue problems is a. 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. Saintvenants principle for sandwich structures springerlink. Venant s theory of torsionflexure is restricted to linearbehavior. Using the saintvenants principle the small central hole will not affect the stress distribution at distances which are large compared with the diameter of the holesay the width of the plate. Use of negative poissons ratio foam as core is possible. For materials like pztsh under prestress, it is shown in 8 that mechanical end effects decay at a. In the absence of body forces, the stresses of primary interest vpx 1, x2 must satisfy the equilibrium equations zp,p 0 in r, 2.
A recently developed eigenfunction expansion method is utilized to obtain threedimensional asymptotic stress field in the. Saint venants principle saintvenant was a strong proponent of coordinating experimental and practical work with theoretical study. In doing so, we have unknowingly been applying saint. End effects for prestressed and prepolarized piezoelectric solids in antiplane shear a. Yang, in basic finite element method as applied to injury biomechanics, 2018. Saintvenant end effects in antiplane shear for classes of. Saintvenants theorem states that the simply connected cross section with maximal torsional rigidity is a circle. A copy of the license is included in the section entitled gnu free documentation license. On saint venant s principle in plane anisotropic elasticity 171 flp avq ap3 aq3 p, q 1, 2, 6, 2. 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 saintvenants principle is considered from the angle of its present practical interest in structural mechanics, especially for composite structures. Saintvenant principle an overview sciencedirect topics.
It is convenient to express these boundary conditions in terms of stresses in the rod. 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. Topic 3 fundamental principles massachusetts institute of. Toupin s version of saint venant s principle in linear elasticity is generalized to the case of linear piezoelectricity. Saintvenants principle and related results for elasticity theory have received considerable attention in the literature but relatively little is known about analogous issues in piezoelectricity. Another issue investigated 8 is that of the influence ofprestress andprepolarization on the rate of stress decay. If you like, in a couple of weeks i can share some of the results. This statement is the simplest manifestation of the socalled saint venants principle. This approach is based on the saint venants principle 5,10,12, which is originally applied in the elasticitys theory. This approach is based on the saint venant s principle 5,10,12, which is originally applied in the elasticity s theory. Ppt saint venants principle powerpoint presentation. 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. In other words, as the distance from the point of loading becomes greater, the local effects are reduced such. 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.
479 319 127 1485 1176 746 608 1171 1109 625 928 386 600 561 733 899 349 1038 1563 66 1183 424 1209 1425 1264 188 1347 1183 593 1029 907 41 770 328 201 461 862 58 1025 1376 1335 192