ANALYSIS OF THERMOELASTIC STRESSES IN LAYERED PLATES

(a)(c)(b)(d)Fig. 7. Stress distributions in the edge region: (a) normal stress σ x , (b) normal stress σ y , (c)normal stress (peeling stress) σ z , (d) shear stress τ zx (MPa)5. CONCLUSIONS1. Using the semi-inverse method, an analyticalsolution is obtained for the thermoelasticproblem of a plate with an arbitrarycontour nonhomogeneous throughthickness. The results are applied foranalysis of a layered plate subjected to auniform temperature change.2. As an application, stresses due to uniformtemperature change in a copper platewith a galvanic steel coating are determined.3. Using the finite element method, thethermo-mechanical state of the same platewith the coating is studied. For the middleregion, good agreement is achieved betweenthe data of the analytical and numericalmethods. The data obtained withthe use of the finite element method forstresses in the edge region of the plate confirmthe validity of the well-known Saint-Venant’s principle.6. REFERENCES1. Feng, Z. C. and Liu, H. D. Generalizedformula for curvature radius and layerstresses caused by thermal strain insemiconductor multilayer structures. J.Appl. Phys., 1983, 54 (1), 83 – 85.2. Hsueh, C. H. Thermal stresses in elasticmultilayer systems. Thin Solid Films,2002, 418, 182 – 188.3. Boley, B. A. and Weiner, J. H. Theoryof Thermal Stresses. John Wiley andSons, Inc., New York, London, 1960.4. Kõo, J. P. Problem of thermoelasticityfor a free nonhomogeneous plate withtemperature variation through thickness.In Heat Stresses in StructuralMembers. Naukova Dumka, Kyiv,1979, 19, 89 – 91 (in Russian).5. Timoshenko, S. P., Goodier, J. N. Theoryof Elasticity. Third Edition.McGraw-Hill, Singapore, 1970.7. CORRESPONDING AUTHORProf. emer. Jakub KõoEstonian University of Life SciencesInstitute of Forestry and Rural EngineeringKreutzwaldi 5, Tartu 51014, Estonia,E-mail: jakub.koo@emu.ee