István Ecsedi

A formulation of the centre of twist and shear for nonhomogeneous beam

In this paper two classical centres related to the problem of transportation of loads applied to one end cross section of a straight prismatic elastic isotropic but nonhomogeneous beam to its fixed other end cross section is analysed. The body forces and lateral surface forces vanish in the both two cases. Our aim is to give the definition and location of centre of twist and shear for nonhomogeneous beam. The material properties of the beam do not depend on the longitudinal coordinate, they may depend only on the cross-sectional coordinates. Formulation of the centre of twist and shear follows considerably the concept of A. Weinstein and E. Trefftz which was used in the case of homogeneous beam.

Elliptic cross section without warping under torsion

Abstract The object of this paper is the pure torsion of the nonhomogeneous anisotropic elastic beam. The results of Saint-Venant’s theory of uniform torsion are used to prove a nonwarping property of elliptic cylinders.

Curved composite beam with interlayer slip loaded by radial load

Abstract Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by a rigid plate and in the second case the radial load is applied immediately to it. The paper gives solutions for radial displacements, slips and stresses. The presented examples can be used as benchmark for the other types of solutions as given in this study.

A Note on the Pure Bending of Nonhomogeneous Prismatic Bars

The paper examines the pure bending of a linearly elastic, isotropic, nonhomogeneous bar. The bending stress, elastic strain energy and the end cross-section rotations are determined for in-plane variation of the Youngs modulus with small strains and displacements. It is shown that the governing formulae for elastic pure bending of nonhomogeneous bars have same forms as formulae for symmetrical bending (bending in the principal planes) of homogeneous bars. Two examples illustrate the application of the developed formulae. In the first, a composite beam is considered; the second deals with the determination of the maximum tensile and compressive stresses in a bent functionally graded elastic bar.

Energy methods for curved composite beams with partial shear interaction

Abstract This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.

Notes on the Centre of Shear

Two methods are known for calculating the position of the shear centre of a bar. By using them we obtain different results. Some authors state that the position of the centre of shear depends on the Poisson ratio, whereas others that it does not. The purpose of this paper is to give a new interpretation for this disagreement.

Bounds for the effective heat conduction coefficient

Abstract The linear problem of the steady-state heat conduction is studied in isotropic nonhomogeneous hollow rigid bodies. Upper and lower bounds are derived for the effective heat conduction coefficient. It is proven that, the effective heat conduction coefficient of a compound body is between the weighted arithmetic and harmonic means of heat conduction coefficients of the homogeneous body components.

Derivation of some fundamental formulae of strength of materials by energy method

In this paper, three fundamental formulae of strength of materials are derived by the application of the theorem of minimum of strain energy. In the first example the torsion of non-homogeneous circular bar is considered. The second example deals with the in-plane bending of non-homogeneous curved beam. The third one is concerned with the pure bending of non-homogeneous elastic prismatic bars.

Saint–Venant torsion of anisotropic elliptical bar

The object of this article is the Saint–Venant torsion of anisotropic, homogeneous bar with solid elliptical cross section. A general solution of the Saint–Venant torsion for anisotropic elliptical cross section is presented and some known results are reformulated. The case of non-warping cross section is analysed.

The Generalized Twist for the Torsion of Piezoelectric Cylinders

In the classical theory of elasticity, Truesdell proposed the following problem: for an isotropic linearly elastic cylinder subject to end tractions equipollent to a torque , define a functional on such that , for each , where is the set of all displacement fields that correspond to the solutions of the torsion problem and depends only on the cross-section and the elastic properties of the considered cylinder. This problem has been solved by Day. In the present paper Truesdell’s problem is extended to the case of piezoelastic, monoclinic, and nonhomogeneous right cylinders.