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The numerical solution of 3‐D thermoelastic problems using only Laplace operator discretization methods
Author(s) -
Fanelli Michele A.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620250216
Subject(s) - thermoelastic damping , discretization , mathematics , laplace transform , operator (biology) , polygon mesh , laplace's equation , mathematical analysis , geometry , thermal , partial differential equation , physics , biochemistry , chemistry , repressor , meteorology , transcription factor , gene
The application of potential theory to the solution of theory of elasticity problems harks back to an old tradition, witness the Boussinesq treatment of the half‐space point loading. In a preceding study by the authour, 1 it has been shown how plane thermoelastic problems can be solved by using only numerical methods suited to treat the Laplace operator Δ 2 φ, hence by introducing only one d.o.f. or every node of the discretization. In the present paper it is proposed to show how similar techniques can be used in a three‐dimensional case. The reduction achieved in the number of nodal unknowns is from three d.o.f. to one; thus it is hoped that—notwithstanding the greater complexity of the present treatment—a computational advantage can be gained over the direct approach, at least for discretization meshes of a few thousands of nodes (which is not unusual for 3‐D domains). The basic formulation draws from fairly classical works 2–6 and differs from more recent ones (e.g. Goodier as quoted in Reference 7) insofar as the particular solutions of the thermoelastic problems do not ntail, in the present approach, any integration, but rather are expressed directly in terms of the thermal field.