{"id":241740,"date":"2020-11-23T00:00:00","date_gmt":"2020-11-22T23:00:00","guid":{"rendered":"https:\/\/cimne.com\/sin-categoria\/pere-andreu-ubach-defends-his-phd-thesis-about-a-bezier-enhanced-shell-triangle\/"},"modified":"2025-09-30T15:46:55","modified_gmt":"2025-09-30T13:46:55","slug":"pere-andreu-ubach-defends-his-phd-thesis-about-a-bezier-enhanced-shell-triangle","status":"publish","type":"post","link":"https:\/\/cimne.com\/es\/pere-andreu-ubach-defends-his-phd-thesis-about-a-bezier-enhanced-shell-triangle\/","title":{"rendered":"Pere Andreu Ubach defends his PhD Thesis about A Bezier-enhanced shell triangle"},"content":{"rendered":"

On November 18th 2020, Pere-Andreu Ubach<\/strong><\/a> has successfully defended his PhD Thesis entitled: \u00abBEST: Bézier-Enhanced Shell Triangle. A new rotation-free thin shell finite element\u00bb<\/strong><\/a>. The thesis has been developed in the framework of the PhD Programme in Structural Analysis<\/strong><\/a> of the Technical University of Catalonia (UPC · Barcelona Tech)<\/strong>. The thesis supervisors have been the UPC professors Eugenio Oñate<\/strong> <\/a>and Julio García-Espinosa<\/strong><\/a>. Due to the COVID-19 restrictions, the thesis defense took place in the online mode. The thesis obtained a qualification of Excellent.<\/strong><\/p>\n

The PhD Exam Committee was formed by Professors Riccardo Rossi<\/a> of UPC · Barcelona Tech (Chair)<\/strong>, Roland Wüchner<\/a> (Braunschweig University, Germany)<\/strong> and Carlos Lázaro<\/a> (Technical University of Valencia, Spain).<\/strong><\/p>\n

Pere-Andreu Ubach<\/strong> has been working as a research engineer at CIMNE during his PhD studies. During this period he has been responsible for the development of several research projects<\/strong>, as well as for the supervision of the construction of two CIMNE buildings at UPC.<\/strong><\/p>\n

\"Ubach
From left to right:<\/strong> Pere Andreu Ubach, Riccardo Rossi and Eugenio Oñate. The image projected shows Professors Julio García-Espinosa, Carlos Lázaro and Roland Wuchner during the on-line presentation.<\/span><\/p>\n

About the thesis<\/h3>\n

A new thin shell finite element is presented. This new element has not rotational degrees of freedom.<\/strong> Instead, in order to overcome the C1 continuity requirement across elements, the author resorts to enhance the geometric description of the flat triangles of a mesh made out of linear triangles, by means of Bernstein polynomials and triangular Bernstein-Bézier patches.<\/p>\n

In order to use them to define the Bernstein-Bézier patches.<\/strong> Ubach, Estruch and García-Espinosa performed a comprehensive statistical comparison of different weighting factors. They find a new weighting factor, wich reduces by about 10% the root mean square error in the estimation of normals of randomly generated surfaces with respect to the previous best weighting factor found in the literature.<\/p>\n

A new paradigm is presented consisting on the reconstruction of the geometry of a cubic triangular element.<\/strong> This geometric reconstruction exploits the properties of cubic B-spline functions (cubic Bézier triangle). This way, the author builds a conforming continuum-based shell finite element.<\/p>\n

The only degrees of freedom of the BEST element are the vertices’ coordinates (9 variables). The remaining 21 parameters are solved internally<\/strong>, introducing energy minimization considerations. In order to fix the values of these 21 internal parameters, each BEST element solves 9 systems of linear equations of rank 3.<\/p>\n

The BEST element is successfully applied to the analysis of thin shells in linear and geometrically non-linear regimes using an implicit method.<\/strong> The non-linearity is solved using a Total Lagrangian formulation. The author succeeds at pre-integrating through-the-thickness efficiently and accurately.<\/span><\/p>\n

The numerical examples results show that the BEST element has the potential to achieve cubic convergence.<\/strong> For membrane oriented tests with curvature, the convergence is quadratic.<\/p>\n","protected":false},"excerpt":{"rendered":"

On November 18th 2020, Pere-Andreu Ubach has successfully defended his PhD Thesis entitled: \u00abBEST: Bézier-Enhanced Shell Triangle. A new rotation-free thin shell finite element\u00bb. The thesis has been developed in the framework of the PhD Programme in Structural Analysis of the Technical University of Catalonia (UPC · Barcelona Tech). The thesis supervisors have been the UPC […]<\/p>\n","protected":false},"author":1,"featured_media":241741,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","slim_seo":{"title":"Pere Andreu Ubach defends his PhD Thesis about A Bezier-enhanced shell triangle - CIMNE","description":"On November 18th 2020, Pere-Andreu Ubach has successfully defended his PhD Thesis entitled: \"BEST: Bézier-Enhanced Shell Triangle. A new rotation-free th"},"footnotes":""},"categories":[46,35],"tags":[147,158,185,180,177],"class_list":["post-241740","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","category-research-news","tag-cimne","tag-civil-engineering","tag-research-overview","tag-researchers","tag-science-for-society"],"acf":[],"_links":{"self":[{"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/posts\/241740","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/comments?post=241740"}],"version-history":[{"count":0,"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/posts\/241740\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/media\/241741"}],"wp:attachment":[{"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/media?parent=241740"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/categories?post=241740"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cimne.com\/es\/wp-json\/wp\/v2\/tags?post=241740"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}