Mathematical linguistics models that can be useful for controlling FE mesh generation are presented in the paper. The problems concerning an application of formal grammars for this purpose are outlined. Advantages and drawbacks related to the use of various types of Lindenmayer string/graph systems applied recently for FE mesh generation are discussed. An efficient (parsable) class of ETPL(k) graph grammars is proposed as a formal tool in this research area.

The paper deals with the optimization of regular space trusses with fixed external dimensions under uniform snow and dead-weight loading. Attempts are being made to find such a number of truss joints which minimise the material volume. The set of constraints imposed on a structure includes the effect of the loss of stability of the compressed bar. The statical problem of shallow domes including geometrical nonlinearity was solved by using the Newton-Raphson iteration procedure.

Interference effects in centers of "disk-like" solid cylinders of different photoelastic materials loaded by uniaxial forces acting along diameters was subject of study. An analysis of the intensity of light passing through the cylinder was carried out, and a few numerical models of the phenomenon were constructed and compared with the experimental results. The dispersive character of the "photoelastic constant" is shown and its consequence for the effect are emphasized. A computer aided spectrometer was specially constructed for the research as "the heart" of a semi-automatic measurement stand. The utilization of the effect for the construction of the optical force sensor is mentioned.

Rectangular cross-sections of reinforced concrete beams and columns with nonsymmetric reinforcement are considered in the paper. The~objective function represents the total cost of concrete, steel and formwork. Several dimensional and behavioral constraints (bearing capacity, cracking, deflection) are allowed for. The problem was formulated in general form so that introduction of specific regulations following from national codes is possible. The computer program for optimal design of beams and frames loaded in-plane has been developed. The numerical examples were computed taking into account the rules of Polish Design Code.

In the presented work a model of a layered, delaminated composite beam based on the finite elements method was introduced. In this model the beam was divided into finite elements, while the delamination was modelled using additional boundary conditions. One delaminated region in the cross-section of the beam was considered which extended to the full width of the beam. It was also assumed that the delamination was open. The influence of the delamination length and position on the changes of natural frequencies of flexural vibrations of the laminated composite cantilever beam were investigated.

A multi-disciplinary, numerical approach to shape optimization of notches is presented. The design of the optimal shape of notches in 2-D elastic machine (structural) components is formulated using the Fictitious Stress Method. The design objective is to minimize the maximum effective stress for a given load. Formulation is based on constant stress boundary element. A special concept of segmented Bezier interpolants is adopted for defining geometry of the machine component, and the Sequential Linear Programming is used as optimization procedure.

The flow formulation for metal forming analysis based on a rigid-viscoplastic material model is considered. Specifically, sensitivity evaluation techniques are discussed for different solution variables with respect to variations in parameters entering the constitutive (and other) equations such as material constants, imposed velocities or friction coefficient. A method to avoid spurious pressure modes is introduced which allows to use Q1/Q1 elements and thus to accurately calculate pressures, their sensitivities and friction forces. Also, not only spurious modes are eliminated but, in addition, one pressure unknown for each node is available in this method, thus yielding a finer discretisation for this variable.