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Current Mechanics and Advanced Materials

Editor-in-Chief

ISSN (Print): 2666-1845
ISSN (Online): 2666-1853

Research Article

Advanced Thick FGM Plates-Cylindrical Shells in Linear Unsteady Supersonic Flow

Author(s): Chih-Chiang Hong*

Volume 3, 2024

Published on: 12 January, 2024

Article ID: e120124225624 Pages: 14

DOI: 10.2174/0126661845283999231214113735

Price: $65

Abstract

Introduction: Thick functionally graded (FG) plates-cylindrical shells with third-order shear deformation theory (TSDT) of displacement models under thermal vibration in linear unsteady supersonic flow are investigated by using the generalized differential quadrature (GDQ) method.

Method: The nonlinear coefficient term of TSDT models and the advanced nonlinear shear correction coefficient expression are used to study the thermal vibration of thick FG plates and cylindrical shells in linear unsteady supersonic flow. At the intersection of FG plates-cylindrical shells, the displacements, stress resultants, and moment resultants could be reasonably assumed in the continuity condition for the differential volume in linear unsteady supersonic flow, respectively.

Result: The dynamic equilibrium differential equations of thick FG plates and cylindrical shells in linear unsteady supersonic flow, respectively in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads consist of the linear supersonic aerodynamic pressure and inertia terms can be presented. Two parametric effects including environment temperature and functionally graded material (FGM) power law index on the thermal stress and center displacement of thick FG plates-cylindrical shells in linear unsteady supersonic flow are investigated.

Conclusion: The linear unsteady supersonic flow over the outer surface of thick FG platescylindrical shells provides the additional aerodynamic effect on the values of displacements and stresses.


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      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select a.nid,a.publish_on, a.pmid,a.article_id,a.doi,j.journal_id,j.subtitle,v.volume_name,a.volume_id as volume_id, a.issue_id,a.title,first_page, last_page, page_count,abstract,ifnull(is_abstract,"y"),asec.title as article_section,at.type_name as article_type_name, a.article_id as ArticleID ,is_epub,epub_price,epub_type,a.created, y.year from `article` as `a` left join `article_section` as `asec` on `asec`.`art_sec_id` = `a`.`is_epub` left join `article_type` as `at` on `at`.`art_type_id` = `a`.`art_type` left join `journal` as `j` on `j`.`journal_id` = `a`.`journal_id` inner join `volume` as `v` on `a`.`volume_id` = `v`.`volume_id` inner join `year` as `y` on `v`.`year_id` = `y`.`id` where a.article_status != "W" and a.is_epub = 4 and a.journal_id = 183 and a.is_uploaded = 1 group by `a`.`article_id` order by `a`.`publish_on` desc
      940μsalphaeurekaselec_live_10_06_2022Article.php#528
      Backtrace
      • 13. app/Models/Article.php:528
      • 14. app/Http/Controllers/ArticleController.php:2071
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select pdf, html, epub, prc from `article_metrics` where `article_id` = 137349 limit 1
      190μsalphaeurekaselec_live_10_06_2022Article.php#744
      Bindings
      • 0: 137349
      Backtrace
      • 14. app/Models/Article.php:744
      • 15. app/Http/Controllers/ArticleController.php:2091
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from content_by_diseases where content_id = 137349 and content_type = 'article' order by status desc limit 1
      320μsalphaeurekaselec_live_10_06_2022Article.php#751
      Backtrace
      • 11. app/Models/Article.php:751
      • 12. app/Http/Controllers/ArticleController.php:2094
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `node_meta` where `nid` = 225624 limit 1
      210μsalphaeurekaselec_live_10_06_2022Meta.php#30
      Bindings
      • 0: 225624
      Backtrace
      • 14. app/Models/Meta.php:30
      • 15. app/Http/Controllers/ArticleController.php:2101
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `bo`.* from `bundle_offer` as `bo` where `bo`.`bundle_status` = 'A' order by `bo`.`bundle_id` desc
      220μsalphaeurekaselec_live_10_06_2022BundleOffer.php#57
      Bindings
      • 0: A
      Backtrace
      • 13. app/Models/BundleOffer.php:57
      • 14. app/Http/Controllers/ArticleController.php:2108
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `tbl_ht_submission` as `h` where `h`.`subtitle` = 'CMAM' and (h.proposal_closing_date = 0 OR TO_DAYS(FROM_UNIXTIME(h.proposal_closing_date)) >= TO_DAYS(NOW())) order by `h`.`manuscript` asc
      250μsalphaeurekaselec_live_10_06_2022Article.php#2025
      Bindings
      • 0: CMAM
      Backtrace
      • 13. app/Models/Article.php:2025
      • 14. app/Http/Controllers/ArticleController.php:2112
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from journal_access where content_type_id = '137349' and content_type = 'a' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      510μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ArticleController.php:2186
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from journal_access where content_type_id = '13408' and content_type = 'i' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      400μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ArticleController.php:2207
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select count(*) as total_count, content_type_access_id as access_type from journal_access where content_type_id = '3442' and content_type = 'v' and ( (from_date <= CURDATE() and to_date >= CURDATE() and perpetual= 0) or (from_date is null and to_date is null and perpetual= 1) )
      370μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
      Backtrace
      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ArticleController.php:2231
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"volume" as access_level,"" as issue_id,"" as article_id from `user_access_journal_volume_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 3442) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"volume" as access_level,"" as issue_id,"" as article_id from `user_access_journal_volume_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 3442) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"volume" as access_level,"" as issue_id,"" as article_id from `user_access_journal_volume_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.volume_id = 3442)
      4.16msalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ArticleController.php:2272
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"issue" as access_level,j.issue_id,"" as article_id from `user_access_issue_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.issue_id = 13408) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"issue" as access_level,j.issue_id,"" as article_id from `user_access_issue_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.issue_id = 13408) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"issue" as access_level,j.issue_id,"" as article_id from `user_access_issue_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.issue_id = 13408)
      590μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ArticleController.php:2297
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"article" as access_level, j.issue_id, j.article_id from `user_access_article_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.article_id = 137349) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"article" as access_level, j.issue_id, j.article_id from `user_access_article_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.article_id = 137349) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"article" as access_level, j.issue_id, j.article_id from `user_access_article_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51716822 and j.to_ip >=51716822 )) and ((j.from_date <= 1739972548 and j.to_date >= 1739972548 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.article_id = 137349)
      600μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ArticleController.php:2329
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `article` where `first_page` < '17' and is_uploaded = 1 and issue_id = 13408 order by cast(first_page as SIGNED) desc limit 1
      460μsalphaeurekaselec_live_10_06_2022Article.php#1819
      Bindings
      • 0: 17
      Backtrace
      • 14. app/Models/Article.php:1819
      • 15. app/Http/Controllers/ArticleController.php:2470
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select * from `article` where `last_page` > '30' and is_uploaded = 1 and issue_id = 13408 order by cast(first_page as SIGNED) asc limit 1
      380μsalphaeurekaselec_live_10_06_2022Article.php#1831
      Bindings
      • 0: 30
      Backtrace
      • 14. app/Models/Article.php:1831
      • 15. app/Http/Controllers/ArticleController.php:2472
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `language_id` from `multilanguage` where `short_code` = 'en'
      210μsalphaeurekaselec_live_10_06_2022ArticleController.php#2497
      Bindings
      • 0: en
      Backtrace
      • 14. app/Http/Controllers/ArticleController.php:2497
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select `source_lang_label`, `target_lang_label` from `multilanguage_labels` where `target_lang_id` = 1
      230μsalphaeurekaselec_live_10_06_2022MultiLanguage.php#23
      Bindings
      • 0: 1
      Backtrace
      • 13. app/Models/MultiLanguage.php:23
      • 14. app/Http/Controllers/ArticleController.php:2498
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select `id` from `multilanguage_article` where `article_id` = 137349 limit 1
      2.45msalphaeurekaselec_live_10_06_2022ArticleController.php#2506
      Bindings
      • 0: 137349
      Backtrace
      • 16. app/Http/Controllers/ArticleController.php:2506
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` inner join `journal` as `j` on `j`.`journal_id` = `bd`.`content_id` where `b`.`banner_journal` = 1 and `bd`.`content_type` = 'J' and `bd`.`content_id` = 183 and `b`.`banner_from_date` <= 1739972548 and `b`.`banner_to_date` >= 1739972548 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.18msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: J
      • 2: 183
      • 3: 1739972548
      • 4: 1739972548
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` inner join `journal` as `j` on `j`.`journal_id` = `bd`.`content_id` where `b`.`banner_journal` = 1 and `bd`.`content_type` = 'J' and `bd`.`content_id` = 183 and `b`.`banner_from_date` <= 1739972548 and `b`.`banner_to_date` >= 1739972548 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.14msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: J
      • 2: 183
      • 3: 1739972548
      • 4: 1739972548
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='458ae4d893457b00e8c094045338c0cb'
      250μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\MultiLanguage
    1MultiLanguage.php#?
        _token
        1s6E9cy7YbBIO2zU3ktsWLWFI8I5mbAFJ5f3a8CH
        uc_cart_id
        458ae4d893457b00e8c094045338c0cb
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/article/137349" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /article/137349
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
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