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. Saint venant s principle and the plane elastic wedge saint venant s principle and the plane elastic wedge the stress field due to selfequilibrating loading on the inner or outer arc of a plane strain elastic wedge sector is affected by two agencies. Pdf saintvenants principle and end effects in anisotropic. Saintvenants principle and end effects in anisotropic. Pdf saintvenants principle and end effects in anisotropic elasticity. The statement of modified saint venants principle is suggested. A study of saint venant s principle for composite materials by means of. Saintvenants principle for a piezoelectric body siam. The steel rod is attached to a rigid plate on the top of the pipe. The axisymmetrical deformation of the infinite circular cylinder loaded by an equilibrium system of forces on its near end is discussed and its formulation of modified saint venants principle is established.
The assumption of a uniform normal stress distribution is valid if the resultant internal force is applied at the centroid of the cross section. Dec 31, 2018 saintvenant s 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 or rational saint venants principle with relaxed boundary condition is developed to generalize the principle and promote its applications to. Saint venants principle saint venants principle saint venant 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 other words, when we calculate stress by conventional methods, i. Components used in any system are subjected to various actual or probable forces. According to saint venant s principle, the calculation model was 22m wide and 24m high, which was divided into 8448 elements. Saintvenant end effects in antiplane shear for classes. Saintvenant principle an overview sciencedirect topics. Jul 26, 2006 2006 saint venant end effects for plane deformations of linear piezoelectric solids.
This is used very frequently in engineering modelling. Svs principle states that when moving away from the ends, the exact. Saintvenants principle in anisotropic elasticity theory. Venants principle, the stress will be concentrated near the point of application of load. In the following section, we describe the traction boundary value problem of plane strain. A proper assessment of end or edge effects in such structures is of fundamental technological importance. Saintvenants principle in dynamics of structures applied. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Saint venant s principle is important in the application of elasticity solutions in many practical situations in which boundary conditions are satisfied in the sense of resultants rather than pointwise. Using the saint venant s principle, show that such a corrective solution may be generated using a simple strength of materials approximation incorporating axial and bending stresses of the form. This paper is concerned with investigation of the effect of mechanicalelectrical coupling on the decay of saint venant end effects in linear piezoelectricity.
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. End effects for plane deformations of an elastic anisotropic semi. On saintvenants principle in linear elastodynamics springerlink. 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. Pdf in this paper, we demonstrate that the neglect of elastic end effects, usually justified by appealing to saint venant s principle, cannot be. Hence there has been continued interest in investigation of the issues underlying this principle, both from a mathematical and physical point of view. Introduction the classical germainkirchhoff theory of thin elastic plates is known to be the leading term of an interior or outer asymptotic expunsion in. According to this principle, the strains that are produced in a body. On saintvenants principle in linear elastodynamics. Determine the displacement at the end of the rod at point c. The result indicates that care must be exercised in predicting the extent of end effects in anisotrop ic solids. Venants principle for plane elasticity problems involving. Using principal centroidal x,yaxes, show how these constants could be determined. The horizontal displacements of both lateral boundaries of the model were restricted, the top of the model was applied the.
Consider first the case of an axial resultant end loading p p z e 3 and m 0. Describe a principle that we call saint venant s principle, and then to employ those stress concentration factors to calculate maximum stresses at discontinuities in structural and machine elements. Saint venant s principle state that if the forces acting on a small portion of the surface of an elastic body are replaced by another statically equivalent system of forces acting on the same portion of the surface, this redistribution of loading. And so, for axially loaded beams, we had assumed that there was average uniform stress over. Since these considerations are related to what is called saint venant s principle we conclude with a discussion of this principle. Closure to discussion of vibration of a group of circular cylinders in a confined fluid 1978, asme j. For stress edgedata, saintvenants principle has frequently been invoked e. Citeseerx saintvenants principe of the problem of the. Article information, pdf download for saintvenant end effects in composites. In the linear theory of elasticity, saintvenants principle is used to justify the neglect of edge effects when determining stresses in a body. I am presently working on distributing some high seismic brace forces to the spillway piers of a dam. The justification for consideration of load resultants is usually based on some form of saint venants principle characterizing the boundary layer behavior involved.
Saintvenant effects in the iosipescu specimen fabrice. Saintvenant end effects for materials with negative poissons ratios. Saint venants principle and end effects in anisotropic elasticity. 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. Saintvenants principle for antiplane shear deformations of. The brass pipe section ab has an outside diameter of 75 mm and thickness of 4 mm. Saintvenants principle and end effects in anisotropic elastic. Citeseerx modified saintvenants principe with example. Saint venants principle and end effects in anisotropic elasticity a commentary has been published. In contrast to the usual case of rapid stress decay. See 1214 for a view of results on saint venants principle. 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. 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.
If you like, in a couple of weeks i can share some of the results. The two papers in which this idea was first exploited in connection with saint venant s principle were those of toupin 1, who treated the cylinder problem, and knowles 2, who dealt with similar issues in the theory of plane strain. Knowles, on saint venant s principle in the twodimensional linear theory of elasticity. Applications of analogical rational saint venants principle and constraintfree ratio. The justification of this approximation is usually based on some form of the celebrated saint venant s principle covering primarily the period 19651981 was given by horgan and knowles. Saint venants principle and boundary conditions theory of.
Saint venants principle saint venant 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. Article concentrates on isotropic homogeneous linear elastic response over a range of structural geometries including waveguides, with either free or constrained lateral surfaces, half space, wedges and cones. 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. Introduction to saint venant s principle and stress concentrations. 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. Pdf 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. Saint venants principle and boundary conditions theory. Hence there has been continued interest in investigation of the issues underlying this principle, both from. 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. In this article, saint venant end effects for selfequilibrated external forces in cosserat solids are investigated for twodimensional case.
In the linear theory of elasticity, saint venants principle is used to justify the neglect of edge effects when determining stresses in a body. On saintvenants principle in plane anisotropic elasticity. And so, for axially loaded beams, we had assumed that there was average uniform stress over the cross sectional area. Materials journal of composite msu college of engineering. Saintvenant end effects in composite structures sciencedirect. Strength of materials mechanics of materials mechanicalc.
Since that time, several developments have taken place demonstrating continued interest in understanding the ramifications of saint venant s principle from. Applying and interpreting saintvenants principle comsol blog. Let an elastic body with lame constants x and v occupy a region d with piecewise smooth boundary i\ in the absence of body. Of course the class of elasticity problems governed by a single second order partial differential equation is limited. Axial loading saint venants principle stress concentrations shearing strain poissons ratio multiaxial loading. Saintvenants principle and the plane elastic wedge. Saint venant, a french mathematician, discussed the above principle for stress distributions in 1864. Venant s principle in justifying a partial model of the dam that only encompasses the spillway piers. Solution of saint venants equation to study flood in rivers.
Saintvenants principle for antiplane shear deformations. Recent developments concerning saintvenants principle citeseerx. Saint venants principle for the axisymmetrical deformation of the circular cylinder and prove its modi. Saint venant principle an overview sciencedirect topics. Since then there has been a great deal of work on this problem and related ones. Saintvenant s 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. Recent developments concerning saintvenants principle. Sep 17, 2016 summary boundary conditions can be conveniently divided into two types for consideration. Saint venant end effects for materials with negative poissons ratios. The dynamic wave, for instance, considers all the terms of the momentum equation. I am doing a finite element model of the piers and am making use of st. Pdf on saintvenants principle in linear elastodynamics. 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. Horgan and carlsson, 2000 but it is only relatively recently that analogous questions for piezoelectricity have been investigated.
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