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.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).