A number of new methods and computational procedures have been developed after World War II. Building of damaged cities and enterprises in such huge extent all over the world necessitated using of new methods and ideas in all areas of human activities. The theoretical treatments were supported in those years by new very effective tools – computers. New numerical methods developed for computers allowed scientists and engineers to solve very complicated and complex problems from practice.

The problems that were unsolvable to this time by classical analytical methods. The finite element method created in that time has become very effective and most spread computational method. Nowadays, it is used in all research and design centers all over the world. Besides solution of problems of elasticity, many other physical problems are solved by this treatment: electromagnetic fields, fluid flow, thermal flow, crack spreading, problems of quantum mechanics and so on. In principle, we are able to solve every problem which is described by differential equation. The finite element method has applications in diverse areas of human activities, in mathematics, physics, medicine, or economy. As curiosity we can mentione its application in the assessment of share prices on stock-market. The limitations of the finite element method led to the creation of other similar treatments and variants of basic procedures: boundary element method, finite volume method, spectral element method, meshless methods, transfer matrix method and so on. Every of these methods has some advantages and drawbacks and accordingly every methods has its own area of application. However, also combinations of these methods are often used in commercial programs.
Besides of above mentioned procedures, the research is now oriented to the solution of nonlinear problems. These problems encompass all types of nonlinearities: geometrical, physical as well as nonlinearity induced by boundary conditions. As a rule, the problems of modern industry are often connected with solution of the so-called multiphysical fields that include several physical phenomena, e.g. microelectromechanical systems, nanoelectromechanical systems, piezoelectricity, nanofluid flow, stability problems and so on. The trend is to simulate diverse materials with different structure and behavior. Simulation can be accomplished in nanoscale, mesoscale, microscale or macroscale and the processes can describe mixture of several basic material types such as elastic, plastic, viscoplastic, or different types of anisotropy and it can encompass more complicated phenomena, e.g. phase transition of material elements.
New methods of computation continuum mechanics allow us to solve huge variety of problems in very specific fields of engineering. These methods accelerated progress in the area of research and everyday engineering practice by fact that automation of engineering design simplifies the work of engineers.

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ams 2 2016


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