Contents of the Journal of Mechanical Engineering 48, 4 (1997)

OKROUHLIK, M.,  HOSCHL, C.: Numerical methods in mechanics of solids.
Part II. Tasks, procedures, and templates                               217 



TONDL, A.: Method of extreme values mapping (in Czech)                  248



KAMINSKI, H., STEFANIAK, J.: The method of potential used 
for  identification of boundary conditions in heat conduction   
                                                                        259



MAUNDER, E. A. W.: Recovery of equilibrium in finite element models 
of stiffened structures                                                 271



LABAS, V., TRNOVCOVA, V.: Residual stresses and toughness of oriented 
eutectic composites (in Slovak)                                         284

A review of numerical methods based on matrix algebra is presented, especially of methods of solution of algebraic equations, generalized eigenvalue problems, solution of differential equations describing transient phenomena, and methods for the solution of nonlinear problems.

The aim of this contribution is to show advantage of the method for the analysis of non-linear oscillatory systems. The principles and different possibilities of using this method are presented. Some illustrative examples confirm its suitability for the analysis of non-linear oscillations, especially of the non-periodic ones. The method enables to investigate the vibration character, to follow the influence of different parameters of the quenching effectiveness of different means on the vibration of a certain coordinate of the system.

In this paper an application of the method of potential is considered for solution of the following inverse problem: On a closed curve \partial\Omega^* \subset \Omega, where \Omega is the region under consideration, temperature T(x^*,t) is prescribed. Assuming that the boundary condition is of the first kind, the temperature at the boundary is to be found. After discretisation in time one obtains a recurrent set of Helmholtz equations instead of parabolic equations with nonhomogeneous initial conditions. Introduction of integral potentials leads to a set of integral equations for the potential density. In the next step, a linear change of temperature on triangular elements is assumed. Then, one obtains a set of algebraic equations instead of integral ones. The solution of a direct and an inverse boundary-value problem for a rectangle is presented as an example.

A methodology is proposed for recovering strong equilibrium from finite element models of stiffened structures which are based on conforming displacement elements or hybrid elements. A procedure is described as an extension of one established for models of continua, and it considers the balancing of stiffener forces and plate tractions separately. A simple 2-D example, the Peery problem, is used for illustration.

A model for prediction of residual strain and stress arising after fabrication of eutectic composites is presented in this paper. The influence of the microstructure, composition, and crystallographical orientation on the distribution of the residual stresses in the composites LiF-TbF₃ is determined by the Finite Element Method. The anisotropy of both elastic properties and thermal expansion coefficients is assumed. The result of the computing shows that the anisotropy of the physical properties can cause a higher toughness in these systems. The effect of the microcracking and deflection of the crack is correlated with the result of the simulation.