This thesis is concerned with modeling, analysis and applications of one-dimen\u00adsional continua and networks thereof. More precisely, we use the pre-curved and -twisted three-dimensional geometrically exact beam theory to rigorously deduce several well-known models: the pre-curved two-dimensional geometrically exact beam, the pre-curved and -twisted three-dimensional linear Timoshenko beam, as weil as the geometrically nonlinear truss and string.<\/p>\n
Based on the abstract theory of first-order quasilinear hyperbolic systems, we show in the second part of this thesis local exact boundary controllability and observability for the second-order system of pre-curved two-dimensional geome\u00adtrically exact beams. Additionally, we formulate an optimal control problem for this system, derive the adjoint equation and identify conditions, that allow for classical adjoint states.<\/p>\n
The one-dimensional models given in this thesis are used in different applications. First, we develop a numerical scheme that solves the optimal control problem for two-dimensional geometrically exact beams. Subsequently, we employ the concept of energetic homogenization to determine effective material properties of a Kirchhoff-Love plate from networks of linear Timoshenko beams and optimize their geometry. With a similar idea, applied at two levels, non-periodic networks of nonlinear strings are homogenized in order to match the behavior of non-woven fiber mats. Finally, the damaging of high-pressure pipes is investigated, which requires a nonlinear path-dependent material law coupled to the three-dimensional geometrically exact beam. In this scenario a creep-damage material law is modeled, numerically implemented and its feasibility to describe piping systems demonstrated.<\/p>","protected":false},"excerpt":{"rendered":"
Die vorliegende Arbeit befasst sich mit der Modellierung, Analyse und Anwendung eindimensionaler Kontinua und Netzwerken daraus. Wir verwenden insbesondere die Theorie vorgekr\u00fcmmter und -verdrillter dreidimensionaler geometrisch exakter Balken, um einige wohlbekannte Modelle rigoros abzuleiten: den vorgekr\u00fcmmten zweidimensionalen geometrisch exakten Balken, den vorgekr\u00fcmmten und -verdrillten dreidimensionalen linearen Timoshenko-Balken, sowie geometrisch nichtlinearen Stab und Saite. Basierend auf […]<\/p>\n","protected":false},"featured_media":2650,"comment_status":"open","ping_status":"closed","template":"","meta":{"_acf_changed":false},"product_brand":[],"product_cat":[60],"product_tag":[],"class_list":{"0":"post-1876","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-fau-studies-mathematics-physics","7":"has-post-title","8":"has-post-date","9":"has-post-category","10":"has-post-tag","11":"has-post-comment","12":"has-post-author","13":"","15":"first","16":"instock","17":"taxable","18":"shipping-taxable","19":"purchasable","20":"product-type-simple"},"acf":{"autor":"Strohmeyer, Christoph","orcid":"","ror":"","herausgeber":"","orcid_hrsg":"","rorhrsg":"","bearbeiter":"","sonstige_beteiligte_personen":"","untertitel":"","zusatz":"","jahr":"2018","zeitschrift":"","serie":"","serie_name":"","serie_band":"","serie_jahr":"","serie_titel_band":"","vortrage":"","issn":"","isbn":"","isbn13":"978-3-96147-137-9","seiten":"283","sonstiges":"","band":14,"auflage":"","opus":"","dspace":"10187","e-isbn_pdf":"978-3-96147-138-6","doi":"https:\/\/doi.org\/10.25593\/978-3-96147-138-6","epub":"","e-isbn_epub":"","doi_epub":"","html":"","e-isbn_html":"","doi_html":"","e-isbn_reader":"","doi_reader":"","digibib":"","urn":"urn:nbn:de:bvb:29-opus4-101877","supplementary_material":"","sprache":["Englisch"],"ausgabe":"Softcover","suche":" 9783961471379 9783961471386 ","lizenz":"BY-4","bemerkung":""},"builder_content":"","_links":{"self":[{"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/product\/1876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/comments?post=1876"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/media\/2650"}],"wp:attachment":[{"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/media?parent=1876"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/product_brand?post=1876"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/product_cat?post=1876"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/www.university-press.fau.de\/en\/wp-json\/wp\/v2\/product_tag?post=1876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}