Sudhir B. Railkar

Specially tailored transfinite-element formulations for hyperbolic heat conduction involving non-Fourier effects

The phenomenon of hyperbolic heat conduction in contrast to the classical (parabolic) form of Fourier heat conduction involves thermal energy transport that propagates only at finite speeds as opposed to an infinite speed of thermal energy transport. To accommodate the finite speed of thermal wave propagation, a more precise form of heat flux law is involved, thereby modifying the heat flux originally postulated in the classical theory of heat conduction. As a consequence, for hyperbolic heat conduction problems, the thermal energy propagates with very sharp discontinuities at the wave front. The primary purpose of the present paper is to provide accurate solutions to a class of one-dimensional hyperbolic heat conduction problems involving non-Fourier effects that can precisely help understand the true response and furthermore can be used effectively for representative benchmark tests and for validating alternate schemes. As a consequence, the present paper purposely describes modeling/analysis formulatio...

Nonlinear/linear unified thermal stress formulations: Trans-finite element approach

Abstract A new unified computational approach for applicability to nonlinear/linear thermal Structural problems is presented. Basic concepts of the approach including applicability to nonlinear and linear thermal structural mechanics are first described via general formulations. Therein, the approach is demonstrated for thermal stress and thermal-structural dynamic applications. The proposed transfinite element approach focuses on providing a viable hybrid computational methodology by combining the modeling versatility of contemporary finite element schemes in conjunction with transform techniques and the classical Bubnov-Galerkin schemes. Comparative samples of numerical test cases highlight the capabilities of the proposed concepts.

A generalized hybrid transfinite element computational approach for nonlinear/linear unified thermal-structural analysis

Abstract The paper describes the development of a new hybrid computational approach for nonlinear/linear thermal-structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements with transform methods and the classical Bubnov-Galerkin schemes. Application of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capabilities of the proposed hybrid transfmite element methodology.

Evaluation of thermally induced non-Fourier stress wave disturbances via tailored hybrid transfinite element formulations

Abstract The evaluation of thermally induced stress wave propagation in solids and materials influenced by non-Fourier effects is described. Several pathological anomalies exist for the classical dynamic thermoelastic models using the Fourier heat conduction model, especially for cases involving extremely short transients or for temperatures near absolute zero. As a consequence, various modified theories have been proposed to account for finite speeds of thermal stress wave propagation, in contrast to investigations based on the classical thermoelastic theory, which allows thermal disturbances to propagate only at infinite speeds. The dynamic thermoelastic models used herein can be obtained from those of Green and Lindsay, which permit the so-called ‘second sound’ effects by appropriate choice of relaxation parameters. The fundamental purpose of this study is to provide accurate solutions to a class of thermally induced non-Fourier models in dynamic thermoelasticity which can help us to understand the representative behavior of the nature and mechanisms of the resulting thermal stress wave disturbances. In this regard, the present paper uses specially tailored hybrid formulations based on the transfinite element approach for accurately modeling the discontinuous thermal stress wave disturbances. The classical Fourier models of dynamic thermoelasticity which can be obtained by appropriate choice of relaxation parameters are also presented. The results obtained indicate that significant thermal stresses may arise because of non-Fourier effects, especially when the speeds of propagation of the thermal and stress waves are equal. For the case of unequal speeds of propagation, the relative magnitudes of the resulting thermal stress waves seem comparable to a certain extent with those obtained from the classical theory of dynamic thermoelasticity.

On heat displacement based hybrid transfinite element formulations for uncoupled/coupled thermally induced stress wave propagation

Abstract The present paper describes the evaluation of heat displacement based hybrid transfinite element formulations for their applicability to coupled/uncoupled thermally induced stress wave propagation problems. The hybrid formulations developed herein utilize the concept of heat displacement which is related to temperature changes in the manner mechanical displacement is related to strain. Therein, transform methods in conjunction with classical Galerkin schemes and contemporary finite element formulations are employed for predicting the dynamic response of coupled/uncoupled thermally induced stress wave propagations. In particular, the test cases analyzed pertain to the well-known Danilovskayas models of coupled/uncoupled thermoelasticity. Applicability to these models is demonstrated via a unified hybrid thermal-structural approach, thereby retaining the advantages of heat displacement and transfinite element formulations.

Hyperbolic heat conduction with convection boundary conditions and pulse heating effects

This paper describes the numerical simulation of hyperbolic heat conduction with convection boundary conditions. The effect of a step heat loading, a sudden pulse heat loading, and a pulse internal heat source are considered in conjunction with convection boundary conditions. Two methods of solution are presented for predicting the transient behavior of the propagating thermal disturbances. In the first method, MacCormacks predictor-corrector method is employed for integrating the hyperbolic system of equations. Next the transfinite element method, which employs specially tailored elements, is used for accurately representing the transient response of the propagating thermal wavefronts. The agreement between the results of various numerical test cases not only validates the representative behavior of the thermal wave fronts but also provides an understanding of the representative behavior due to convection boundary conditions and varied heating effects.

Hybrid transfinite element methodology for nonlinear transient thermal problems

Abstract A new transfinite element methodology for nonlinear transient thermal analysis is described. The proposed methodology is a hybrid approach that combines the major advantages of finite-element techniques, classical Bubnov-Galerkin schemes, and transform methods. Fundamental concepts of the methodology, including recent developments for application to nonlinear thermal problems, are described in technical detail. The applicability of the hybrid transfinite element approach to nonlinear transient thermal problems is quite novel. Comparative results of several test problems validate the basic capabilities of the proposed formulations. The hybrid transfinite element approach proposed here provides a computational methodology for nonlinear transient thermal analysis and has the potential for further extension.

Special purpose hybrid transfinite elements and unified computational methodology for accurately predicting thermoelastic stress waves

Abstract This paper represents an attempt to apply extensions of a hybrid transfinite element computational approach for accurately predicting thermoelastic stress waves. The applicability of the present formulations for capturing the thermal stress waves induced by boundary heating for the well known Danilovskayas problems is demonstrated. A unique feature of the proposed formulations for applicability to Danilovskayas problem of thermal stress waves in elastic solids lies in the hybrid nature of the unified formulations and the development of special purpose transfinite elements in conjunction with the classical Galerkin techniques and transformation concepts. Numerical test cases validate the applicability and superior capability to capture the thermal stress waves induced due to boundary heating.

Evaluation and applicability of hybrid transfinite-element formulations with particular reference to radiation

Abstract The evaluation and applicability of hybrid transfinite-element formulations are described for transient nonlinear thermal models with particular reference to radiation effects. The formulations are developed from basic concepts and evaluated for both one- and two-dimensional thermal models. The methodology presented is a hybrid approach, in that it combines finite elements, classical Galerkin schemes, and transform methods. Basic features of the hybrid formulations and the associated solution scheme are first described. Therein, numerical test models are presented to evaluate the applicability for predicting the nonlinear transient response in one- and two-dimensional thermal models influenced by radiation effects.

A hybrid transfinite element approach for nonlinear transient thermal analysis

A new computational approach for transient nonlinear thermal analysis of structures is proposed. It is a hybrid approach which combines the modeling versatility of contemporary finite elements in conjunction with transform methods and classical Bubnov-Galerkin schemes. The present study is limited to nonlinearities due to temperature-dependent thermophysical properties. Numerical test cases attest to the basic capabilities and therein validate the transfinite element approach by means of comparisons with conventional finite element schemes and/or available solutions.