A PROCEDURE BASED ON FINITE-ELEMENTS FOR THE SOLUTION OF NONLINEAR PROBLEMS IN THE KINEMATIC ANALYSIS OF MECHANISMS

In the present paper the kinematic analysis oi. mechanisms is based on the application of finite elements is discussed. It is shown how the kinematic properties of the rigid-body motions of a mechanism can be o btained from an analysis of the stiffness matrix of a simple model com prising rod-type elements in the case of planar mechanisms. In the eve nt that there is also a more complex finite element model of the mecha nism, one may in addition obtain the node values from the results achi eved with the simple model. Special attention is given to nonlinear po sition problems, i.e. initial, successive, deformed, and static equili brium. An error function is provided that is valid in each case, This function is derived from the elastic potential function, and uses Lagr ange multipliers and penalty functions, The result is an application o f the primal-dual method, or augmented Lagrange multipliers (ALM) meth od. This function is minimized by means of Newton's method, which lead s in simple form to the vector gradient as a force vector. The second- derivative matrix is derived from the stiffness matrix, to which a com plementary matrix owing to the nonlinearity introduced by the large di splacements is added. This method can be easily implemented on a compu ter. The computer program will be able to perform a wide variety of ki nematic analyses of any planar mechanism with lower pairs. The models of the mechanisms are very simple, and need only a few tens of degrees of freedom even for the most complex mechanisms. The CPU time is also very low due to the simplicity of the method and its good convergence properties.