Stress–temperature equations of motion of Ignaczak and Beltrami–Michell types in arbitrary curve coordinate system: معادلات الحركة بلغة الإجهادات والحرارة من نوعي إغناتشاك وبيلترامي– ميشيل في أي نظام احداثي منحني

Abstract

This paper relates to the mathematical linear model of the elastic, homogeneous and isotropic body, with neglected structure and infinitesimal elastic strains, subjected to temperature field; discussed by Hooke, and shortly called (H). We firstly introduce the variable tensorial forms of the traditional and Lame descriptions of the coupled dynamic state of considerable Hooke body, in an arbitrary curve coordinate system. We study the variable tensorial forms in an arbitrary curve coordinate system, of the generalized Beltrami–Michell stress-temperature equations, and of the stress-temperature Ignaczak equations and its completeness problem for the (H) thermoelastic body.