{"id":333,"date":"2019-11-04T14:51:55","date_gmt":"2019-11-04T14:51:55","guid":{"rendered":"http:\/\/inverseprobleme.de\/?page_id=333"},"modified":"2020-01-06T21:14:59","modified_gmt":"2020-01-06T21:14:59","slug":"damage-monitoring-of-elastic-structures","status":"publish","type":"page","link":"http:\/\/inverseprobleme.de\/?page_id=333&lang=en","title":{"rendered":"damage monitoring of elastic structures"},"content":{"rendered":"\n

In many industrial productions fiber composites are of growing interest and used in ever more diverse setups. For example in aircraft and wind power plant construction carbon reinforced fiber composites are nowadays of utmost importance. These high-performance materials are very costly. Hence, for safety and especially from an economic point of view, it is important to detect damages as soon as possible before greater parts of a structure deteriorate.<\/p>\n\n\n\n

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Source: Wikipedia<\/a><\/figcaption><\/figure>\n<\/div>\n\n\n\n
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Source: Wikipedia<\/a><\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n

Traditional materials such as\nsteel change slowly from an elastic to plastic deformation. Fiber composites\nhowever behave very differently. Small delaminations of single layers or growth\nof fissures can barely be seen by naked eye but might lead to severe damages or\nfailure of the structure. Hence, the development of robust and reliable Structural\nHealth Monitoring (SHM) systems are important to enhance safety and to decrease\nmaintenance intervals and, lust but not least, costs at the same time. A SHM system\nconsists of a network of piezo-ceramic sensors and actuators that are attached\nto the structure\u2019s surface (see sketch below). The sensors then measure signals\nthat come from the actuators, travel through the entire structure and interact\nwith possible defects. <\/p>\n\n\n\n

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Sketch of a SHM system consisting of 3 actuators and 3 sensors applied on a structure with a damage (delamination)<\/figcaption><\/figure><\/div>\n\n\n\n

The mathematical model of wave\npropagation in elastic structures is given by Cauchy\u2019s equation of motion which\nis, depending on the applied constitutive law, a linear or nonlinear hyperbolic\nsystem of PDEs with initial and boundary values. A SHM system has to solve the inverse problem<\/strong> of computing parameters\nof the PDE, such as, e.g., the modulus of elasticity or the stored strain\nenergy function, from sensor data that are acquired at the surface. Because of\nits nonlinearity, time-dependency and high dimensionality this inverse problem\nis amongst the most challenging tasks in this area. A reconstruction of a damage\nbased on the Landweber iteration can be seen in the figure below, where the\nyellow dots mark the sensor positions.<\/p>\n\n\n\n

\"Schadensdeketion
Reconstruction of a delamination (red circle) in a transversly isotropic structure; the sensor positions are marked in yellow<\/figcaption><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"

In many industrial productions fiber composites are of growing interest and used in ever more diverse setups. For example in aircraft and wind power plant construction carbon reinforced fiber composites<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-333","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=\/wp\/v2\/pages\/333","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=333"}],"version-history":[{"count":11,"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=\/wp\/v2\/pages\/333\/revisions"}],"predecessor-version":[{"id":506,"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=\/wp\/v2\/pages\/333\/revisions\/506"}],"wp:attachment":[{"href":"http:\/\/inverseprobleme.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}