Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_5
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Ordinary Differential Equations","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_5","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_5","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115672267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_10
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Peridynamic Least Square Minimization","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_10","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_10","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128712206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_6
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Partial Differential Equations","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_6","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_6","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114313365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_7
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Coupled Field Equations","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_7","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_7","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"265 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123112003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_8
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Integrodifferential Equations","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_8","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_8","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131641077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_2
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Peridynamic Differential Operator","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_2","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_2","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126177147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.
{"title":"Weak Form of Peridynamics","authors":"E. Madenci, Mehmet Dorduncu, A. Barut, N. Phan","doi":"10.2514/6.2018-1223","DOIUrl":"https://doi.org/10.2514/6.2018-1223","url":null,"abstract":"This chapter presents the weak form of the peridynamic (PD) governing field equations. They specifically concern the Poisson’s equation and Navier’s equation under in-plane loading conditions. Their weak forms derived based on the variational approach enable the direct imposition of nonlocal essential and natural boundary conditions. The numerical solution to these equations can be achieved by considering either a uniform or a nonuniform discretization.","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"100 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125970137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-02647-9_4
E. Madenci, A. Barut, Mehmet Dorduncu
{"title":"Interpolation, Regression, and Smoothing","authors":"E. Madenci, A. Barut, Mehmet Dorduncu","doi":"10.1007/978-3-030-02647-9_4","DOIUrl":"https://doi.org/10.1007/978-3-030-02647-9_4","url":null,"abstract":"","PeriodicalId":129456,"journal":{"name":"Peridynamic Differential Operator for Numerical Analysis","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115436905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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