SENSITIVITY ANALYSIS OF 3D FRICTIONAL CONTACT WITH BEM USING COMPLEXSTEP DIFFERENTIATION
THIS PAPER IS A STUDY ON THE APPLICATION OF THE COMPLEX STEP DIFFERENTIATION METHOD ON A PARAMETER SENSITIVITY ANALYSIS FOR A 3D ELASTIC CONTACT PROBLEM. THE ANALYSIS IS PERFORMED WITH BOUNDARY ELEMENT METHOD (BEM) WITH DISCONTINUOUS ELEMENTS, ALONG WITH THE GENERALIZED NEWTON METHOD WITH LINE SEARCH (GNMLS). A STANDARD BEM IMPLEMENTATION IS USED, AND THE CONTACT RESTRICTIONS ARE FULFILLED THROUGH THE AUGMENTED LAGRANGIAN.THIS METHOD IN CONJUNCTION WITH BEM ALLOWS TO SKIP THE CALCULATION OF THE NON-LINEAR DERIVATIVES DURING THE SOLUTION PROCESS, ALLOWING FOR A FAST AND RELIABLE SOLUTION PROCEDURE. THE PARAMETER SENSITIVITY IS EVALUATED USING COMPLEX-STEP DIFFERENTIATION. THIS WELL KNOWN METHOD APPROXIMATES THE DERIVATIVE OF A FUNCTION ANALOGICALLY TO THE STANDARD FINITE DIFFERENCES METHOD, WITH THE ADVANTAGES OF BEING NUMERICALLY EXACT, AND NEARLY INSENSITIVE TO THE STEP-SIZE. A HERTZ TYPE PROBLEM IS SOLVED, AND THE PARAMETER EVALUATED IS THE YOUNG MODULUS AND ITS INFLUENCE ON THE MAXIMUM CONTACT PRESSURE, AND COMPARED WITH ANALYTIC SOLUTIONS.
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