Journal of Theoretical and Applied Mechanics

Volume 33, Number 4, 2003





G. Gospodinov

University of Architecture, Civil Engineering and Geodesy,


1, Christo Smirnenski Blvd., 1046, Sofia, Bulgaria,






Abstract. In this paper the boundary element method is developed for thermoelastic stress analysis of plane sheets of arbitrary geometry and boundary conditions. The steady state temperature field is considered to be known or calculated in advance. Although a linear elastic solution is employed, an elevated temperature procedure is applied and at certain stage brittle, traction free cracks may develop, typical for a quasi-brittle type of materials, such as concrete. A special type of displacement discontinuity fundamental solution is used in order to include the crack opening into the boundary element solution. In the appendix a few approaches to reducing domain integrals into boundary ones only are given for the most general cases of the temperature distribution function.



Key words: boundary elements, thermo-elasticity, crack opening.






Keramische Werkstoffe und Bauteile, University of Bremen,


Am Biologischen Garten 2 / IW3, D-28359 Bremen, Germany,



G. B. Stoychev

Technical University Sofia,


8, Kl. Ohridski Blvd., 1756 Sofia, Bulgaria,




Yield criterion for pressure sensitive materials


Abstract. A new yield criterion for pressure sensitive materials is proposed. The criterion is based on the first invariant of the stress tensor, second and third invariants of the stress deviator tensor and includes three material constants. In the space of the principal stresses the criterion can be represented as a smooth and convex surface, opened in the negative direction of the hydrostatic axis. Convexity conditions are formulated for anelastic solid. Based on experimental data the validity of the criterion in a case of two dimensional stress state is shown for grey cast iron.


Key words: yield criterion, elastic-plastic material, grey cast iron.


Alexander Zlatarski

Industrial Heat Engineering Branch, NIPRORUDA JSCo

205, Al. Stamboliyski Str., 1309 Sofia, Bulgaria,

Angel Baltov

Institute of Mechanics, Bulgarian Academy of Science,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,





Abstract. The effect of harmonic heating of high-alloy and high-carbon steel ingots on the homogeneous Chromium distribution in alloying elements is investigated. The effect of the higher temperature of the ingot core due to the harmonic thermal regime is estimated.



Key words: harmonic heating, chromium homogenization, high-alloy and high-carbon steel.


N. G. Gospodinov

Technical University of Sofia,

8, Kl. Ohridsky Blvd., 1756 Sofia, Bulgaria


On the Relationships between Linear and Angular Strains in Twisting

Abstract. Based on an experimental approach, the applicability of two logarithmic expressions for the relationships: "True angular strain technical angular strain", on the one hand, or "true angular strain relative angular strain" on the other hand, is determined for twisting of plastic materials up to the occurrence of fracture. The theoretical relationships "twisting moment (or tangential stress) angular strain" are compared with curves obtained experimentally.


Key words: technical angular strain, relative linear strain, true angular strain, true linear strain.



G. Stoychev

Technical University of Sofia,

8, Kl. Ohridski Blvd., 1756 Sofia, Bulgaria,



Modelling elastoplastic deformations

in grey cast iron


Abstract. Elasto-plastic deformation of grey cast iron is in consideration. A non-associated constitutive model, based on the phenomenological approach is proposed. The yield condition is established on the second invariant of the stress deviator, on the first invariant of the stress tensor. The plastic potential is based on the same invariants. Modified form of the plastic work is defined as a hardening parameter and tensile test curve is used to calculate it. An algorithm of the computer procedure is given to compute the strains if the principal stresses are known. The verification of the model is realized by bi-axial tests on tubular specimens.



Key words: constitutive laws, elastic-plastic materials, grey cast iron, mechanical testing



P. Dineva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria,


F. Vaccari, G. Panza

Department of Earth Sciences, University of Trieste,

Via Weiss 4, 34127, Trieste, Italy,



Hybrid Modal Summation-BIE Method for Site Effect Estimation of a Seismic Region in a Laterally Varying Media

Abstract. A new hybrid MS-BIE method based on the modal summation (MS) and the boundary integral equation (BIE) methods is developed. The proposed hybrid technique allows the theoretical seismogram synthesis taking into consideration seismic source properties, non-homogeneous wave path and local site effects as layering with non-parallel interfaces and free-surface topography. Each of the two techniques is applied in the part of the structural model where it works more efficiently. The MSM is applied for numerical simulation of wave propagation from the source position to the local region of interest, while the BIEM is used inside the local multilayered geological region. The accuracy and validation study of the proposed method is presented by solution of numerical examples simulating different seismic scenarios. The comparison between the MS-BIEM synthetic seismograms and ones obtained by pure analytical and/or other hybrid methods has been evaluated and discussed.


Key words: modal summation method, boundary integral equation method, seismic source, non-homogeneous wave path, local multrilayered geological region, synthetic seismograms.