A mixed variational method for linear coupled thermoelastic analysis

Abstract A variational method for linear coupled quasi-static thermoelastic analysis is presented. The variational support is a statement in terms of displacement, temperature, stress and heat flux. The statement is based on the hybrid stress formulation for the elastic part and on the mixed flux–temperature formulation for the thermal one, and includes the rate dependent terms of the energy balance equations and the initial condition. A finite element model for the semidiscrete analysis is developed within this variational framework, and a guideline for implementing a family of thermoelastic finite elements is given. Some test cases enlighten the effectiveness and reliability of the approach proposed.

[1]  G. Prathap,et al.  Consistent thermal stress evaluation in finite elements , 1995 .

[2]  S. N. Atluri,et al.  Existence and stability, and discrete BB and rank conditions, for general mixed-hybrid finite elements in elasticity , 1985 .

[3]  Francesco Ubertini,et al.  On the consistency of finite element models in thermoelastic analysis , 2001 .

[4]  Ilya Prigogine,et al.  Thermodynamics of Irreversible Processes , 2018, Principles of Thermodynamics.

[5]  R. E. Nickell,et al.  Approximate Solutions in Linear, Coupled Thermoelasticity , 1968 .

[6]  Tong Earn Tay.  Finite element analysis of thermoelastic coupling in composites , 1992 .

[7]  T. H. H. Pian,et al.  On Hybrid and mixed finite element methods , 1981 .

[8]  G. Altay,et al.  Some variational principles for linear coupled thermoelasticity , 1996 .

[9]  Finite element coupled thermostructural analysis of composite beams , 1997 .

[10]  Booker,et al.  Finite Element Analysis of Coupled Thermoelasticity , 1987 .

[11]  Edward C. Ting,et al.  A finite element formulation for thermal stress analysis. Part I: Variational formulation , 1976 .

[12]  J. Z. Zhu,et al.  The finite element method , 1977 .

[13]  Y. Y. Zhu,et al.  Unified and mixed formulation of the 4‐node quadrilateral elements by assumed strain method: Application to thermomechanical problems , 1995 .

[14]  B. M. Fraeijs de Veubeke,et al.  Dual analysis for heat conduction problems by finite elements , 1972 .

[15]  M. Biot.  Thermoelasticity and Irreversible Thermodynamics , 1956 .

[16]  S. Minagawa,et al.  Transient coupled-thermoelastic problem of heat conduction in a multilayered composite plate , 1992 .

[17]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[18]  Åke Björck,et al.  Numerical Methods , 2021, Markov Renewal and Piecewise Deterministic Processes.

[19]  F. Ubertini,et al.  A hybrid flux model for heat conduction problems , 2000 .

[20]  W. L. Wood.  Practical Time-Stepping Schemes , 1990 .

[21]  A variational principle for the coupled thermoelastic problem , 1968 .

[22]  M. Ben-Amoz,et al.  On a Variational Theorem in Coupled Thermoelasticity , 1965 .

[23]  F. Ubertini,et al.  A hybrid flux axisymmetric model for thermal analysis , 2001 .

[24]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[25]  G. Herrmann.  On variational principles in thermoelasticity and heat conduction , 1963 .

[26]  C. L. Chow,et al.  On invariance of isoparametric hybrid/mixed elements , 1992 .

[27]  William Prager,et al.  Theory of Thermal Stresses , 1960 .

[28]  S. Fenves.  Numerical and computer methods in structural mechanics , 1973 .