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- W134014018 abstract "1. I NTRODUCTION In the paper an approximate solution of the inverse problem of thermal stresses is presented. As the input data the internal temperature responses are used. The aim of this work is to explore the Trefftz functions [1] in this type of inverse problems. Unlike other approximate methods the Trefftz method leads to an approximate solution that satisfies strictly the governing equation and approximately the initial and boundary conditions The method is flexible regarding the initial and boundary conditions. The conditions may be given in the discrete or continuous form, and they even may be incomplete. The obtained approximate solution is continuous with respect to all the variables. Trefftz functions can also be used as shape functions in FEM – the method is then called FEMT. Using FEMT we can built the time-space finite elements with base functions depending in continuous way on time and space variables and – as it is mentioned above – contrary to the classical FEM the obtained solution satisfies the governing equation. In addition, precision of the approximate solution can be improved not only by increasing the node number but also by increasing the degree of approximation. An important asset of the FEMT is the ability to solve inverse problems by using this method. The concept of functions that satisfy a given differential equation and have to be fitted to the governing boundary conditions originates from Trefftz [1]. Trefftz functions (T-functions) for different linear partial differential equations are mainly used to construct an approximate solution of a given problem (a direct or an inverse one) in a form of linear combination of the functions. Such a solution satisfies the governing equation; in order to obtain the best fitting to the initial and boundary conditions a functional describing an inaccuracy of their fulfillment (error functional)" @default.
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- W134014018 date "2009-01-01" @default.
- W134014018 modified "2023-09-30" @default.
- W134014018 title "Trefftz function for solving a quasi-static inverse problem of thermal stresses" @default.
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