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A new original primal-mixed finite element approach and related hexahedral finite element : H CT q for the analysis of behavior of solid bodies under thermal loading is presented. The essential contributions of the present approach is the treatment of temperature and heat flux as fundamental variables that are simultaneously calculated, as well as capability to introduce initial and prescribed temperature and heat flux. In order to minimize accuracy error and enable introductions of flux constraints, the tensorial character of the present finite element equations is fully respected. Moreover, one of the main potentials of the present hexahedral finite element is in overcoming of well-known transition problem of connecting finite elements of different types and dimensions. The main goal of the present investigation is to validate the use of the new finite element : H CT q in steady state heat analysis of isotropic, orthotropic or multi-material solid bodies under different thermal or mechanical loading scenarios. The proposed finite element is subjected to high order test of convergence, as well as some standard benchmark tests in order to test convergence of the results, which enlighten the effectiveness and reliability of the approach proposed.

A new multifield finite element method in steady state heat analysis