Method for numerical solution of fuzzy steady state heat conduction problem based on full grid point collocation theory

Abstract

The invention discloses a method for numerical solution of a fuzzy steady state heat conduction problem based on a full grid point collocation theory. The method comprises the first step of carrying out finite element modeling of a steady state heat conduction structure; the second step of utilizing fuzzy variables to represent uncertain input parameters and then obtaining a fuzzy finite element equation of the heat conduction problem; the third step of utilizing cut set operation to rewrite the fuzzy finite element equation to be a group of interval finite element equations; the fourth step of performing approximate representation on temperature response functions in the interval finite element equations based on a polynomial theory; the fifth step of quickly solving the interval variation range of a temperature response approximate functions according to the full grid point collocation theory; the sixth step of utilizing a fuzzy resolution theory to recombine temperature response intervals under all cut set levels, and finally obtaining a membership function of the fuzzy temperature response. According to the method, the prediction of structure heat conduction temperature field containing fuzzy uncertain parameters can be achieved systematically, and the calculation accuracy can be effectively improved on the premise of guaranteeing that the calculation efficiency meets the engineering requirements, which cannot be achieved through common commercial software.

Description

technical field [0001] The invention belongs to the field of mechanical engineering, and in particular relates to a numerical solution method for a fuzzy steady-state heat conduction problem based on a full-grid collocation theory. Background technique [0002] Heat transfer problems are ubiquitous in engineering. In the fields of automobile manufacturing, electronic engineering, energy and chemical industry, how to realize heat transfer more effectively and make structures and electronic equipment work normally is also an important problem faced by engineers. Especially in the field of aerospace, the coupling effect of heat transfer and structure is more significant. With the continuous advancement of science and technology, the heat transfer system of aircraft is becoming more and more complex, and the performance requirements are getting higher and higher, which makes fine analysis become an important development trend of aircraft design. [0003] From the development of...

AI Technical Summary

Problems solved by technology

In actual engineering, the complexity of the system leads to difficulties and inconveniences in the mathematical expression of physical problems, and it is often necessary to simplify and convert objective uncertain problems into subjective deterministic problems, which leads to Classical calculation and design methods are increasingly unable to meet the requirements of refined analysis and design of complex heat transfer systems

Images