Supervisor: Jaan Lellep (professor, TÜ matemaatika instituut)
Karoly Jarmai (professor, University of Miskolc, Hungary)
Rimantas Kacianauskas (professor, Vilnius Gediminas Technical University, Lithuania)
The current work is devoted to the theory of analysis and optimization of stepped circular and annular plates subject to smooth yield surfaces. Chapter 1 provides the brief historical review of the problem and of the finite element method. The Basic ideas of parallel computation, also of the multigrid method are presented herein, as well. In Chapter 2 a method for numerical investigation of axisymmetric plates subjected to the distributed transverse pressure loading was presented. The material of plates studied herein is assumed to be an ideal elastic plastic material obeying the non-linear yield condition of von Mises and the associated flow law. The strain hardening as well as geometrical non-linearity are neglected in the present investigation. Calculations carried out showed that the obtained results are in good correlation with those obtained by ABAQUS when solving the direct problem of determination of the stress strain state of the plate. In Chapter 3 an analytical-numerical study of annular plates operating in the range of elastic plastic deformations was undertaken. The material of plates was assumed to be an ideal elastic plastic material obeying the Mises yield condition. The author succeeded in the analytical derivation of optimality conditions for this highly non-linear problem. The obtained systems of equations were solved by existing computer codes. In Chapter 4 the methods of analysis and optimization of plates with piece wise constant thicknesses developed earlier for homogeneous isotropic materials are extended to plates made of anisotropic materials. The plastic yielding of the material is assumed to take place according to the criterion Tsai-Wu and the associated gradientality law. The traditional bending theory is used, non-linear effects are neglected in the current study.