zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Nonlinear structural design sensitivity analysis for path dependent problems. I: General theory. (English) Zbl 0724.73158
Summary: Two procedures (direct differentiation and adjoint structure) for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper. Continuum formulation is used and both geometric and material nonlinearities are included in the derivations. Incremental nonlinear analysis based on the total Lagrangian concept is adopted. The reference volume concept is used to unify the shape and nonshape design problems. To show the generality of the theory, the derived expressions are reduced to some special cases that have been treated previously in the literature. In Part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory. The theory has also been discretized elsewhere using finite element approximations for implementation into structural analysis programs. These developments offer a firm foundation for design optimization of complex structural systems.

74P99Optimization in solid mechanics
74H45Vibrations (dynamical problems in solid mechanics)
74S05Finite element methods in solid mechanics