روش جديد حل معادلات سيستم هاي مكانيكي در مسايل معكوس و حذف خطا

A New Method for the Solution of Equations of Mcchanicai Systems in Inverse Problems and Data Filtering

Analysis of mechanical systems usually leads to the solution of a set of simultaneous equations. Very often these equations can be classified as a combination of a group of linear equations in terms of some selected variables and a group of nonlinear equations. This paper presents a new method for the solution of these equations. The method uses any non-iteration technique suitable for the solution of linear group. The nonlinear group, however, is solved by a new formula for the nonlinear variable increments in consecutive iterations. This is based on Taylor series expansion. It is shown that the method is effective with good rate of convergence and needs less number of initial approximations compared with those needed in Newton-Raphson method. The paper also presents a method for removing errors from measured data. The method creates a matrix filter based on the available information about the system involved. These two methods have been described in a simple case study of a simple beam under pure bending. The results of simultaneous identification of modulus of elasticity and removing of errors from measured lateral deflections of the beam prove the effectiveness and accuracy of the proposed methods.