Meshfree Simulation Of The Coupled Stress Theory Considering The Effect Of Temperature Gradient

In the ultra high temperature gradient,ultra high temperature rising rate and strong heat deposition in the special environment,materials exhibit thermal coupling characteristics of complex,traditional thermodynamics theory is not applicable.Even though the thermal stress of elastic mechanics considering the effect of strain gradient,but did not consider the influence of temperature gradient on stress field,the temperature gradient is introduced into the thermal couple stress elastic constitutive relations,and the establishment of meshfree numerical method,the influence of temperature gradient on the mechanical properties of the structure force.The main research work of this paper is as follows:(1)Using Helmholtz free energy function,the influence of temperature gradient on stress field is considered in the constitutive relation of thermoelasticity of couple stress.The temperature gradient is introduced into the constitutive equation of thermoelasticity of couple stress,and a simplified couple stress constitutive relation considering temperature gradient is obtained.In this model,the temperature gradient produces couple stress.(2)Moving least squares approximation can be used to construct shape function conveniently and flexibly,and the shape function has the advantage of high-order continuity.Temperature field and temperature gradient are approximated by moving least squares approximation,strain and rotation curvature are directly differentiated by node displacement.A meshfree computing framework of couple stress theory considering the effect of temperature gradient is established,and Fortran is compiled computing program.(3)The expansion and bending deformations of thin plates under temperature gradient are numerically simulated by using the established meshfree method.The effects of temperature gradient on structural deformations are studied by comparing the calculated results with those without considering the effects of temperature gradient.The effects of scale factors on structural deformations are studied in detail.This paper provides a reference and guidance for the study of thermo-mechanical coupling characteristics of special materials,and provides a new idea for numerical simulation of structures considering the effects of temperature gradient field and strain gradient field.