Attila Baksa

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.

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.

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.

Contact Optimization Problems for Stationary and Sliding Conditions

The contact stress distribution is frequently not regular. It may contain singularities reducing the lifetime of machine elements. In order to eliminate such stress singularities, the application of contact pressure control is recommended in the contact conditions. In the paper, several classes of optimization problems are formulated for stationary and sliding contacts. Further, they are illustrated by specific examples. The relation to wear process is made as a natural way to attain the steady state contact profile satisfying the optimality conditions corresponding to minimization of the wear dissipation rate. It is assumed that the displacements and strains are small and the materials of the contacting bodies are elastic.

A Note on the Shear Formula

In this paper, a non-homogeneous, isotropic, linearly elastic bar of uniform cross-section is considered. The bar is subjected to bending and shear. The modulus of elasticity of the bar is independent of the axial coordinate. A generalization of the classic Jourawski shear formula is presented for bars of non-homogeneous cross-section. The shear formula derived is valid for arbitrary directions of the applied shear force. Three examples illustrate the application of the generalized Jourawski shear formula.