# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics. (English) Zbl 0897.73069
Summary: The scaled boundary finite-element method, alias the consistent infinitesimal finite-element cell method, is developed starting from the governing equations of linear elastodynamics. Only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals must be evaluated. General anisotropic material is analysed without any increase in computational effort. Boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization. This method is exact in the radial direction and converges to the exact solution in the finite-element sense in the circumferential directions. For a bounded medium, symmetric static-stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption. A stress singularity is represented very accurately, as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization.
##### MSC:
 74S05 Finite element methods in solid mechanics 74S15 Boundary element methods in solid mechanics
LAPACK