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Regularity for shearable nonlinearly elastic rods in obstacle problems. (English) Zbl 0915.73078
Summary: Based on the Cosserat theory describing planar deformations of shearable nonlinearly elastic rods, we study the regularity of equilibrium states for problems where the deformations are restricted by rigid obstacles. We start with the discussion of general conditions modeling frictionless contact. In particular, we motivate a contact condition that, roughly speaking, requires the contact forces to be directed normally, in a generalized sense, both to the obstacle and to the deformed shape of the rod. We show that there is a jump in the strains in the case of a concentrated contact force, i.e., the deformed shape of the rod has a corner. Then we assume some smoothness for the boundary of the obstacle and derive corresponding regularity for the contact forces. Finally, we compare the results with the case of unshearable rods and obtain qualitative differences.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
49J40 Variational inequalities
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