TOPOLOGICAL SENSITIVITY ANALYSIS FOR NONLINEAR HYPERELASTICITY PROBLEMS
Keywords:
TOPOLOGICAL OPTIMIZATION, FINITE ELEMENTS, NONLINEAR ELASTICITY, HYPERELASTICITY,Abstract
THE TOPOLOGICAL SENSITIVITY ANALYSIS (TSA) IS REPRESENTED BY A SCALAR FUNCTION, DENOMINATED TOPOLOGICAL DERIVATIVE (TD), THAT GIVES FOR EACH POINT OF THE DOMAIN THE SENSITIVITY OF A GIVEN COST FUNCTION WHEN A INFINITESIMAL HOLE IS CREATED. ITS APPLICATIONS TO LAPLACE, POISSON, HELMOLTZ, NAVIER, STOKES AND NAVIER-STOKES EQUATIONS CAN BE FOUND IN THE LITERATURE. IN THE PRESENT WORK, AN APPROXIMATED TD EXPRESSION APPLIED TO NONLINEAR HYPERELASTICITY PROBLEMS IS OBTAINED BY A NUMERICAL ASYMPTOTIC ANALYSIS. THE COST FUNCTION IS THE TOTAL POTENTIAL ENERGY FUNCTIONAL. THE WEAK FORM OF STATE EQUATION IS THE CONSTRAINT AND THE TOTAL LAGRANGIAN FORMULATION USED. NUMERICAL RESULTS OF THE PRESENTED APPROACH ARE CONSIDERED FOR HYPERELASTIC PLANE PROBLEMS.Downloads
Published
2010-12-21
Issue
Section
Articles
License
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).