# Special Finite Elements with Adaptive Strain Field on the Example of One-Dimensional Elements
## 1 Introduction
These elements have been also applied in structural analysis of shear walls with openings. Typical for super elements is elimination of nodes using the matrix condensation technique. That is why super elements have only four nodes at the corners of a wall panel, but to satisfy the compatibility conditions at the boundaries of the element, so called fictitious beams have to be added. A certain limitation of modelling the structure with use of macromodeling technique is the fact that homogenization of the material properties is required, which is performed on the basis of theoretical assumptions and the results of experimental research. However, micromodeling is based on the analysis of small-sized parts of the constructions, including microscopic structures, and relates only to selected areas of building constructions. Similar to macromodelling, the final finite element is the result of homogenization of various sub-areas. Additionally, the interaction between the components of the microstructure is taken into account, introducing complex interface elements and/or describing non-linear phenomena such as plasticity or cracking [10]. Mostly analysis of microstructure is performed in order to assess influence of microdefects on bearing capacity of building components, on strength of materials and also on potential progress of failure mechanism [11]. A characteristic attribute of the micromodeling technique is the development of a computer model of a single cell of the structure, and then homogenization [12; 13; 14]. Unfortunately, analysis of microstructures with this technique is computationally expensive, which often results in the lack of practical application of this approach in the calculations of large and complex structural models. As heterogeneous materials are largely treated, the materials containing various types of inclusions like in works [15; 16] or holes. Very often, the analysis of structures containing holes or inhomogeneities is the part of the so-called multi-scale modelling. In recent decades, there has been a significant development of methods that take into account the multi-scale nature of materials. An example can be the work [17], where the authors describe the developed element containing an opening and a crack simultaneously. In this work, according to the presented examples, the authors confirm the reduction of finite element number and prove that it has an influence on improved numerical calculations and obtaining a satisfactory accuracy of the results. This is in line with the current trend of searching for methods aimed at limiting the number of finite elements used in calculations. As another example, we mention the work [18], where the numerical implementation of the element with an elliptical hole and crack with a different number of nodes on the edge of the element was presented. In these elements, Trefftz functions were used as test functions for stresses and strains that meet the appropriate differential equations and boundary conditions in advance. These functions make it possible to calculate the stiffness matrix of a finite element by means of integration along the border (edge) of a finite element. [PERSON] and [PERSON] [19] used a hybrid elements with elliptical holes in the calculations of plates in a plane stress state. A plate with a single horizontal, sloping elliptical hole and with two horizontal elliptical holes was analysed. In the work [20], the modified stress functions were presented, that were used in the calculation of the stress distribution in a constrained (finite) plate with a rectangular hole subjected to uniaxial tension. A finite area containing a rectangular opening has been mapped to a finite area containing a single circular opening using the so-called mapping function. The aim of development and implementation of all mentioned elements and also presented in the paper multi-area elements is striving for reduction of elements and nodes number in calculation models.