Arbitrary Plane Systems of Anisotropic Beams

A plane problem of anisotropic elasticity theory on an arbitrary junction of thin beams under the action of mass forces is considered. The lateral sides of the beams are free of loads, and a part of junctions are rigidly fixed. The beams and junctions (clamped, slowly moving, and movable) are classified on the basis of asymptotically exact weighted Korn's inequalities. In the presence of movable beams, a one-dimensional model of a system of beams contains algebraic equations and nonlocal transmission conditions together with conventional differential equations and local transmission conditions. On the basis of a solution to a one-dimensional problem, the leading terms of the elastic-field asymptotics are constructed and estimates for asymptotic remainders are derived.