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Elastostatic analysis of infinite solids using finite elements
Author(s) -
Sharan Shailendra K.
Publication year - 1992
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.1620350107
Subject(s) - finite element method , computation , spring (device) , boundary value problem , point (geometry) , mathematics , constant (computer programming) , mathematical analysis , boundary (topology) , simple (philosophy) , stress (linguistics) , geometry , structural engineering , algorithm , computer science , engineering , epistemology , programming language , philosophy , linguistics
A novel technique is developed to simulate the effects of an infinite elastic solid by using multiple springs having spatially varying stiffnesses. The spring constants are computed by numerical integration of classical solutions for point or line loads in an infinite or semi‐infinite elastic mass. Under certain conditions, even the 'exact' values of spring constants may become negative at some nodes. A simple and highly effective algorithm is proposed to remove this computational difficulty. The technique is applied to the computation of displacements and stresses around underground openings. For a circular opening subjected to different stress conditions, spring constants computed by the proposed numerical integration technique are found to be 'identical' to their 'exact' values. Results obtained by the proposed technique for displacements and stresses around circular and non‐circular openings are found to be in an excellent agreement with classical and boundary element solutions. The principal advantages of the proposed technique are that an unbounded solid may be simulated by a relatively very small finite model and a standard finite element code requires no modification for its implementation.