The second part of the paper presents finite-dimensional models of linear elastic, elastic-strain hardening, elastic-perfectly plastic

and rigid-perfectly plastic structures. These models can be seen as a result of discretisation procedure applied to the models of solids derived in the Part I. The implications of sub-dividing degrees of freedom into those with prescribed external forces and those with given displacements are discussed. It is pointed out that the dual energy principles given in this part of the paper can serve as a direct basis for numerical computations.

This paper presents revised and extended version of theory proposed in the late 1970-ties by A. ˇCyras and his co-workers. This theory, based upon the notion of duality in mathematical programming, allows us to generate variational principles and to investigate existence and uniqueness of solutions for the broad class of problems of elasticity and plasticity. The paper covers analysis of solids made of linear elastic, elastic-strain hardening, elastic-perfectly plastic and rigid-perfectly plastic material. The novelty with respect to ˇCyras’s theory lies in taking into account loads dispersed over the volume and displacements enforced on the part of surface. A new interpretation of optimum load for a rigid-perfectly plastic body is also given.

In a dynamic machining process, distortion in surface irregularity is a very complex phenomenon. Surface irregularities form a periodic representation of the tool profile with various kinds of disturbance in a broad range of changes in the height and length of the profile. To discern these irregularity disturbances, interactions of the tool in the form of changes perpendicular and parallel relative to the workpiece were analyzed and simulated. The individual kinds of displacement of the tool relative to the workpiece introduce distortions in the changes of height and length. These changes are weakly represented in standard height and length irregularity parameters and their discernment has been found through amplitude-frequency functions.

If we throw something into a river, how long will it take to reach a certain location downstream? We talk to Prof. Ian Guymer from the University of Sheffield about our increasingly complex models of this deceptively simple problem.

The problem of determining displacements of objects is an important and current issue, in particular in terms of operational safety. This is a requirement that covers geodetic, periodic control measurements in order to determine horizontal and vertical displacements. The paper is focused on the analysis of vertical displacements. Geodetic measurements and their interpretation allow to reduce the risk of possible structural catastrophes. The major research topic of the majority of available papers is displacement determination of individual controlled points, in a situation where there are identified as fixed reference points. There are cases making identification of such points difficult or impossible to use in displacement analysis. This paper addresses a rare case of determining vertical displacements in unstable reference systems. Due to the fact that most of the existing and known literature methods do not always bring satisfactory results, the paper propose a new method of vertical displacement determination in the absence of reference points in the local coordinate system. Practical considerations on simulated data show that the presented method performs the task correctly.

When it comes to research into changes which took place in Poland in the 10th and the first half of the 11th century and the emergence of the Piast dynasty’s state, the presence of an ethnically foreign population, its conditioning and effects have not been fully recognised. The few historiographical sources do not devote much attention to the arrival of foreign tribes; the single mentions typically pertain to the representatives of the elites, especially dynasties. Attempts have been made to analyse the phenomena by means of toponomastics and archaeology. Due to their ambiguity and late source confirmations, the results of toponomastic surveys do not allow to resolve the issue of migrations or displacement from the 10–11th centuries independently. However, the archaeological research carried out to date has revealed (beside a number of single historical objects related to the culture of Poland’s southern neighbours) grave fields and strongholds which could be potentially related to the representatives of foreign ethnic groups. The Poznań-Sołacz grave field (2nd half of the 10th century) and the Morawy grave field in Kuyavia (2nd half of the 11th century or possibly earlier) are related to a population from (Great) Moravia. Presence of a Hungarian population is traditionally attributed to the “old Hungarian” grave field in Przemyśl-Zasanie (dating back from the late 9th to the first quarter of the 11th century). On the other hand, the stronghold and the grave field in Niemcza in Silesia (dated back to the 970s and 980s) are connected with a Czech population. Unconfirmed grave fields and a handful of artefacts of Great Moravian origin are typical remains of strongholds in Gilów in Silesia and Czerchów near Łęczyca where presence of foreign warriors has not been ruled out. A question remains to what extent the material determinants of a foreign culture indicate presence of representatives of different ethnic groups and to what extent they are imports or copies. Undoubtedly, in a discussion of a foreign population genetic research may prove helpful, especially in grave fields associated with foreign populations. However, in order to analyse the issue in a comprehensive way, an interdisciplinary approach is required i.e. a combination of the methods of historical, archaeological and genetic research.

Oil can be produced from reservoirs by use of primary methods that use natural reservoir drive, secondary methods, involving a physical displacement of oil and tertiary (enhanced), in which additional types of energy support oil recovery. About 25-35% of original oil in place for light and medium oil and about 10% heavy oil could be extracted by primary and secondary methods. Injection of CO2 into the oil fields (CO2-EOR) is one of the tertiary oil recovery method. Carbon dioxide is used for increasing oil extraction due to the fact that: to maintain reservoir pressure, reduces the oil viscosity and facilitates its movement in the reservoir, reduces density and increase the volume of oil, interacts with rocks. Depending on the oil composition and the reservoir pressure and temperature injected carbon dioxide can displace oil from the reservoir miscible or immiscible. Additional 10-20% of the oil extraction over primary and secondary methods recovery can be obtained under the miscibility conditions, in immiscibility condition additional oil production is lower. EOR method selection depends on many geological, reservoir and economic parameters. These include: density, viscosity and composition of the oil, minimum miscibility pressure, the recovery factor and vertical and horizontal reservoir variability. Using the above criteria appropriate EOR method for given oil field can be selected. The five parameters: the reservoir depth, the oil density, pressure and temperature of the reservoir is used for the selection of oil fields suitable for miscible oil displacement.

The paper presents the author’s non-linear FEM solution of an initially stressless deformed flat frame element, in which the nodes are situated along the axis of the bar initially straight. It has been assumed that each node may sustain arbitrary displacements and rotation. The solution takes into account the effect of shear, the geometrical non-linearity with large displacements (Green-Lagrange’s strain tensor) and moderate rotations (i.e. such ones which allow a linear-elastic behaviour of the material) and alternative small rotations when the second Piola-Kirchhoff stress tensor is applied. This solution is based on [1], concerning beams without any initial bow imperfections. The convergence of the obtained results at different numbers of nodes and Gauss points in the element was tested basing on the example of circular arcs with a central angle of 120°÷180°. The analysis concerned elements with two, three, five, seven, nine and eleven nodes, for the same number of points of numerical integration and also with one more or less. Moreover, the effect of distributing the load on the convergence of the results was analyzed.

In the 20th century toponymy of the Kłodzko Land underwent serious changes, which with no doubt can be called a revolution. After 1945 and the displacement of the German population all the pre-war names were substituted with Polish ones, which, unfortunately, only rarely were connected with the former tradition, in some cases as old as the middle ages. Most of new names were introduced by a special commission whose main aim was to mark that the new areas gained by Poland after the World War II (the so called Regained Territories) were successfully taken into possession. However, many places and objects (some mountain tops, rock formations, springs, parts of villages) did not receive a name. In the next decades, new local communities started to accustom the mountainous landscape and independently gave names to various nameless (in Polish) places. Unfortunately, due to the depopulation of rural areas in the Kłodzko Land and other formal reasons, the process was quite slow. The main aim of the paper is not only to analyse those changes, but also to compare the numbers of names in chosen moments of the 20th century. For this purpose three types of maps in 1 : 25 000 scale were used: pre-war (German) “Meßtischblatt”, a Polish topographic map representing the situation at the beginning of the 1970s and, finally, the “Army topographic map” from the end of the 20th century. On the first map 531 geographical names were marked, on the second — only 225, and on the third — 277, which is still approximately half of the number before 1945.