ELASTICITY EQUATIONS FOR SPATIAL CURVED BEAMS WITH LARGE DISPLACEMENT AND SMALL ROTATION

Based on previous researches on curved beams, the paper presents improved equations of elasticity to raise the efficiency of curve structure analysis, and then develops the geometrical non-linear spatial curved beam element. In the aspect of geometry, the geometrical relation between displacement and deformation is expressed by a series of matrix formulas. In the aspect of equilibrium relation, the differential equation for the equilibrium of curved beam is derived using differential geometry theory. The relevant formulas are given in forms of vector and matrix. Then the internal force-displacement virtual work equation is established based on the weighted residual method and the principle of equivalent deformation work. At last, to develop the geometrical non-linear curved beam element, the relationship between section internal force and displacement is proposed from the view of generalized Hooke constitutive relation.