Title

Finite Element Analysis of Thermomechanical Problems

Description

The rate formulation for the quasistatic boundary value problem is rephrased after a brief discussion of "weak coupling" between thermal and mechanical processes. This description of the mechanical problem under non-isothermal conditions forms the basis for the subsequent finite element discretisation (matrix displacement method). First, a number of two dimensional finite element displacement models are investigated in regard to their strain approximation, bearing in mind that no thermal stresses should arise from linear temperature distributions. Subsequently, various possibilities are presented to approximate the spatial distribution of plastic work within higher order displacement models.

After this review of approximation problems, constitutive relations in thermal environments are discussed with special consideration of temperature dependent material properties.

First, the Iinear theory of uncoupled thermoelasticity is restated and extended to non-isothermal problems. For temperature dependent material properties there exists a fundamental difference between the hyper- and hypoelastic description of the material behaviour. Both formulations are discussed and applied to solve the thermoelastic problem of a cylinder with a spherical cavity under transient thermal conditions exhibiting temperature dependent material properties.

Subsequently, the elasto-plastic constitutive law is reformulated to incorporate a temperature dependent loading function. This general material relation is then restricted to the von Mises yield criterion and to the Prandtl-Reuss hardening rule in order to obtain quantitative thermoelasto-plastic stress-strain relations for temperature dependent material properties. Moreover, the formulation is extended to incorporate creep effects, for which the prescribed thermal strains are supplemented by initial creep strains at the beginning of each time interval. The application of this material law to a realistic engineering example is illustrated on a pressure vessel nozzle under steady state conditions exhibiting temperature dependent material properties.

Creator

Argyris, J. H.

Balmer, H.

St. Doltsinis, J.

Willam, K. J.

Abstract

The rate formulation for the quasistatic boundary value problem is rephrased after a brief discussion of "weak coupling" between thermal and mechanical processes. This description of the mechanical problem under non-isothermal conditions forms the basis for the subsequent finite element discretisation (matrix displacement method). First, a number of two dimensional finite element displacement models are investigated in regard to their strain approximation, bearing in mind that no thermal stresses should arise from linear temperature distributions. Subsequently, various possibilities are presented to approximate the spatial distribution of plastic work within higher order displacement models.

After this review of approximation problems, constitutive relations in thermal environments are discussed with special consideration of temperature dependent material properties.

First, the Iinear theory of uncoupled thermoelasticity is restated and extended to non-isothermal problems. For temperature dependent material properties there exists a fundamental difference between the hyper- and hypoelastic description of the material behaviour. Both formulations are discussed and applied to solve the thermoelastic problem of a cylinder with a spherical cavity under transient thermal conditions exhibiting temperature dependent material properties.

Subsequently, the elasto-plastic constitutive law is reformulated to incorporate a temperature dependent loading function. This general material relation is then restricted to the von Mises yield criterion and to the Prandtl-Reuss hardening rule in order to obtain quantitative thermoelasto-plastic stress-strain relations for temperature dependent material properties. Moreover, the formulation is extended to incorporate creep effects, for which the prescribed thermal strains are supplemented by initial creep strains at the beginning of each time interval. The application of this material law to a realistic engineering example is illustrated on a pressure vessel nozzle under steady state conditions exhibiting temperature dependent material properties.

Corporate Author

lnstitut fur Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universitat Stuttgart

Imperial College of Science and Technology, University of London

Report Number

AFFDL TR 71-160 p. 729-771

Report Availability

Full text available

Publisher

Wright-Patterson Air Force Base, OH : Air Force Flight Dynamics Laboratory, Air Force Systems Command and Air Force Institute of Technology, Air University

Date

1973

Type

article

Date Issued

1973-12

Provenance

Bombardier/Aero

Distribution Classification

1

Distribution Conflict

No

DTIC Record Exists

No

Format

1 online resource (42 pages) : ill.

Extent

42

Identifier

AD0785968

Is Part Of

Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971