The theoretical foundations of the FEM in the form of a classical mixed method in the problems of structural mechanics are presented. Based on this theory, algorithms for solving problems of statics, dynamics and stability of structures of various types have been developed, which are not inferior in their simplicity and efficiency to algorithms based on FEM in the form of the displacement method. Examples illustrating the computational algorithm of the FEM in a mixed form are given. The book is intended for researchers, postgraduates, masters and specialists in the field of theory and methods of calculation of complex structures by numerical methods in structural mechanics and mechanics of deformable solids.

The article considers the actual problem of the ecology of urban areas associated with air pollution by industrial and energy enterprises. The study is aimed at substantiating the method of forming a plan for atmospheric air pollution observation using mobile laboratories. The quantitative characteristic of sites for different urban development zones is determined as a set of estimates. The air pollution index was chosen as a total sanitary and hygienic criterion for assessing pollution. The implementation of the decision-making problem using the analytic network process method is considered. Parameters of the city and environment that affect the assessment of atmospheric air quality were selected in the course of the study. A network structure of mutual influence of the studied parameters is formed. The architecture of the decision support system based on the proposed method is given. The created software makes it possible to automate the modeling of the distribution of pollutants in the atmosphere. The computational experiment is presented on the example of the Volgograd agglomeration, Russia. The proposed approach can significantly improve the organization of monitoring by mobile laboratories and reduce the cost of obtaining data on urban air pollution without increasing the number of existing observation laboratories, both stationary and mobile.

The paper gives an algorithm for the analysis of systems with unilateral constraints through the finite element method in the form of a classical mixed method. Given that both displacements and forces are variables in the system of governing equations, the procedure for the incremental parametric loading as a part of the analysis of structurally nonlinear systems allows varying the respective parameter, tending from «hard» loading based on the load parameter towards «soft» loading based on the displacement (configuration) parameter. The efficiency of the algorithm is shown by the example of a beam with unilateral constraints

This paper presents the arguments for the efficiency of the Finite Element Method in the form of the classical mixed method being developed by the authors. The example of a bended plate shows that the system of governing equations of the FEM in this form has the same order as the system of equations of the FEM in displacements. The analysis algorithm is similar to that of the analysis by the FEM in displacements. Since the primary unknowns include both displacements and forces, the analysis returns the values of nodal deflections and bending moments. Test example illustrates good convergence of the numerical results to the exact solution. The further development of this form of the FEM as an alternative to the FEM in displacements is recommended