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Material constraints, Lagrange multipliers, and compatibility. Applications to rod and shell theories. (English) Zbl 0769.73012

The authors deal with the theory of material (internal) constraints in continuum mechanics, formulating a global constraint principle, having a physically and mathematically natural interpretation. An appropriate general role for the Lagrange multipliers as reactive stresses is put into evidence; it is shown for which kind of constraints the global constraint principle reduces to the classic local principle. Applications to rods, shells and discrete models are presented.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K15 Membranes
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