CAJ | 학술논문

以应力张量作为单个应变张量的张量值函数，用张量不变量表示，得到了各向同性材料6阶非线性完备的、不可约的本构模型及其相应的应变能函数。同时，基于张量函数表示定理，研究了自变量为有限应变张量E和温度T，因变量为应力张量K的张量值函数，推导了6阶非线性各向同性弹性材料完备的，不可约的热应力本构方程和应变能函数。由张量函数出发导出的6阶非线性各向同性材料的本构方程，虽然是完备的，不可约的，在任意坐标系下都成立、具有普适性，但是实际应用仍需要转换到特定坐标系，才能同几何方程、平衡方程一起，组成求解弹性力学问题完备的方程组。因此，本文将得到的张量形式的本构方程应用到球坐标系下，得到了薄球壳非线性本构方程以及薄球壳热应力本构方程。同时，推导了薄球壳非线性内力和力矩。
이응력장량작위단개응변장량적장량치함수，용장량불변량표시，득도료각향동성재료6계비선성완비적、불가약적본구모형급기상응적응변능함수。동시，기우장량함수표시정리，연구료자변량위유한응변장량E화온도T，인변량위응력장량K적장량치함수，추도료6계비선성각향동성탄성재료완비적，불가약적열응력본구방정화응변능함수。유장량함수출발도출적6계비선성각향동성재료적본구방정，수연시완비적，불가약적，재임의좌표계하도성립、구유보괄성，단시실제응용잉수요전환도특정좌표계，재능동궤하방정、평형방정일기，조성구해탄성역학문제완비적방정조。인차，본문장득도적장량형식적본구방정응용도구좌표계하，득도료박구각비선성본구방정이급박구각열응력본구방정。동시，추도료박구각비선성내력화력구。
The tensor function as single strain tensor can be expressed as tensor invariant and scalar invariant,and 6-order nonlinear constitutive complete and irreducible equations and corresponding strain energy function of iso-tropic elastic material were deduced. At the same time,the tensor function which independent variables were finite strain tensor E and temperature T was studied based on the law of tensor function expressions,and 6-order nonlin-ear thermal stress constitutive equations and corresponding strain energy function of isotropic elastic material were proposed. 6-order nonlinear constitutive complete and irreducible equation of isotropic material,based on tensor functions,is suitable for arbitrary coordinate system with universal. However,for practical applications,constitutive equations that still need to be converted to a specific coordinate system form complete equations solving elasticity problem with geometric equations and equilibrium equations. Therefore,tensor form of constitutive equations will be applied to the spherical coordinates to got nonlinear constitutive equation and thermal stress constitutive equation of a thin spherical shell. At the same time,the section of non-linear internal force and moment of the thin spherical shell are derived.