A thermodynamically consistent non-linear mathematical model for thermoviscoelastic plates/shells with finite deformation and finite strain based on classical continuum mechanics

摘要: Abstract This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain deformation for thermoviscoelastic plates/shells based on the conservation balance laws of classical continuum mechanics (CCM) in R 3 (see Surana Mathi, (2020) linear theory). The Lagrangian description with measure conjugate stress are considered. pairs second law thermodynamics (SLT), consideration additional physics principle equipresence utilized to determine constitutive variables their argument tensors. theory contravariant Piola–Kirchhoff tensor is derived using Green’s its convected time derivatives up order n as tensors representation theorem complete basis (i.e. integrity). provide ordered rate dissipation mechanism that naturally due measure. heat vector integrity also theory. Simplified forms these theories presented. solution methods mathematical model BVPs well IVPs p -version hierarchical higher degree element method Due dissipation, energy equation integral part accounts mechanical work resulting entropy production, hence heat. plate/shell geometry (flat or curved) described by middle surface containing nodal vectors (at each nine nodes), ends which define bottom top surfaces (Surana 2020). mapped into ξ η ζ natural coordinate space two unit cube. local approximations constructed describe faces controlled -levels , directions (element approximation). presented here accurate very thin thick plate/shells small strains. Non-linear allow more complex behavior term strains rates, mechanism. Dissipation an SLT physics. always ensures thermodynamic equilibrium during evolution it CCM . preserves three dimensional nature regardless thickness locking problems shear correction factors plague most currently used formulations.