{"id":14796,"date":"2022-12-24T14:55:00","date_gmt":"2022-12-24T12:55:00","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=14796"},"modified":"2022-12-26T21:12:38","modified_gmt":"2022-12-26T19:12:38","slug":"programna-realizacziya-iteraczijnyh-algorytmiv-dlya-rozvyazannya-ploskoyi-fizychno-nelinijnoyi-zadachi","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=14796","title":{"rendered":"\u041f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0430 \u0440\u0435\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u0456\u0442\u0435\u0440\u0430\u0446\u0456\u0439\u043d\u0438\u0445 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0456\u0432 \u0434\u043b\u044f \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0430\u043d\u043d\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0457 \u0444\u0456\u0437\u0438\u0447\u043d\u043e \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0437\u0430\u0434\u0430\u0447\u0456"},"content":{"rendered":"

<\/p>\n

\u041f\u0420\u041e\u0413\u0420\u0410\u041c\u041d\u0410 \u0420\u0415\u0410\u041b\u0406\u0417\u0410\u0426\u0406\u042f \u0406\u0422\u0415\u0420\u0410\u0426\u0406\u0419\u041d\u0418\u0425 \u0410\u041b\u0413\u041e\u0420\u0418\u0422\u041c\u0406\u0412 \u0414\u041b\u042f \u0420\u041e\u0417\u0412\u2019\u042f\u0417\u0410\u041d\u041d\u042f \u041f\u041b\u041e\u0421\u041a\u041e\u0407 \u0424\u0406\u0417\u0418\u0427\u041d\u041e \u041d\u0415\u041b\u0406\u041d\u0406\u0419\u041d\u041e\u0407 \u0417\u0410\u0414\u0410\u0427\u0406<\/p>\n

SOFTWARE IMPLEMENTATION OF ITERATIVE ALGORITHMS FOR SOLVING A PLANAR PHYSICALLY NONLINEAR PROBLEM<\/p>\n

\u00a0<\/strong>\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 108-112. \u041d\u043e\u043c\u0435\u0440: \u21165, 2022 (313)\u00a0\u00a0\"\"<\/a> <\/strong>
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2022-313-5-108-112<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438: <\/strong>\u0411\u0410\u0413\u0420\u0406\u0419 \u041e\u043b\u0435\u043d\u0430
\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nORCID ID: 0000-0003-2267-7162<\/a>
\ne-mail: bahriio@khmnu.edu.ua
\nBAHRII Olena
\nKhmelnytskyi National University<\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u0420\u043e\u0437\u0433\u043b\u044f\u0434\u0430\u0454\u0442\u044c\u0441\u044f \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438\u0439 \u0431\u043b\u043e\u043a \u0434\u043e \u0441\u043f\u0435\u0446\u0456\u0430\u043b\u0456\u0437\u043e\u0432\u0430\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e\u0433\u043e \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u0443 GEO, \u0449\u043e \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454 \u0432\u0440\u0430\u0445\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u043e\u0441\u043e\u0431\u043b\u0438\u0432\u043e\u0441\u0442\u0456 \u0434\u0435\u0444\u043e\u0440\u043c\u0443\u0432\u0430\u043d\u043d\u044f \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0430 \u0442\u0430 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u0442\u0438 \u043f\u0440\u043e\u0446\u0435\u0441 \u0434\u0435\u0444\u043e\u0440\u043c\u0443\u0432\u0430\u043d\u043d\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0457 \u043e\u0431\u043b\u0430\u0441\u0442\u0456, \u0437\u0430\u043f\u043e\u0432\u043d\u0435\u043d\u043e\u0457 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0438\u043c \u043c\u0430\u0442\u0435\u0440\u0456\u0430\u043b\u043e\u043c.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0456\u0442\u0435\u0440\u0430\u0446\u0456\u0439\u043d\u0438\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438\u0439 \u0431\u043b\u043e\u043a, \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0435 \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0435, \u0432\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0454 \u0442\u0435\u0440\u0442\u044f.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

To solve physically nonlinear problems, specialized software solutions based on the procedures of MSE, FDM, BEM, etc. are used. The article provides an overview of software complexes that allow solving problems in various fields of science and technology. To solve a planar physically nonlinear problem, it is irrational to use the considered systems in most cases since they are closed software complexes, making it impossible to modify the algorithm partially. The difference between software systems is only in the “nonlinear” part, where a specific algorithm for solving a specific problem is implemented. The proposed software implementation of iterative algorithms for solving a plane physically nonlinear problem consists of several independent modules, each of which performs a separate calculation stage. The principle of the iterative algorithm is that a complex physically nonlinear problem is solved step by step. At each stage, a linear problem is solved, in which the values of the deformation parameters are assigned depending on the level of stresses and strains in each element reached at the previous stage. The iterative algorithm is implemented based on the specialized GEO software package developed at the Department of Strength of Materials of KhNU. The complex implies the possibility of replacing a “nonlinear” program block, depending on the type of nonlinear relations adopted in the model. The nonlinear block considered the features of the deformation of a discrete medium, namely, the accepted nonlinear dependencies of a particular material. In the calculation process, the divergence with the linear solution is checked at each iteration until the required accuracy is achieved. This allows simulating the deformation process of a flat area filled with a discrete material.
\nKeywords:<\/strong> iterative algorithm, non-linear program block, discrete environment, internal friction.<\/p>\n

\u041b\u0456\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/strong><\/p>\n

    \n
  1. \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438\u0439 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441 SolidWorks. URL: https:\/\/www.solidworks.com\/<\/li>\n
  2. PLAXIS Geotechnical Analysis Software. URL: https:\/\/www.bentley.com\/en\/products\/brands\/plaxis<\/li>\n
  3. \u0410\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u043e\u0432\u0430\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043d\u0430\u0443\u043a\u043e\u0432\u0438\u0445 \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u044c (\u0410\u0421\u041d\u0414) \u00abVESNA\u00bb. URL: https:\/\/www.knuba.edu.ua\/ukr\/?page_id=934<\/li>\n
  4. \u0411\u0430\u0433\u0430\u0442\u043e\u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438\u0439 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441 \u041b\u0406\u0420\u0410-\u0421\u0410\u041f\u0420. URL: https:\/\/www.liraland.ua\/lira\/<\/li>\n
  5. SCAD Office. \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441 SCAD \/ \u0412. \u0421. \u041a\u0430\u0440\u043f\u0438\u043b\u043e\u0432\u0441\u043a\u0438\u0439, \u042d. \u0417. \u041a\u0440\u0438\u043a\u0441\u0443\u043d\u043e\u0432, \u0410.\u00a0\u0410.\u00a0\u041c\u0430\u043b\u044f\u0440\u0435\u043d\u043a\u043e, \u041c. \u0410. \u041c\u0438\u043a\u0438\u0442\u0430\u0432\u0440\u0435\u043d\u043a\u043e, \u0410. \u0412. \u041f\u0435\u0440\u0435\u043b\u044c\u043c\u0443\u0442\u0435\u0440, \u041c. \u0410. \u041f\u0435\u0440\u0435\u043b\u044c\u043c\u0443\u0442\u0435\u0440. \u2013 \u0421\u041a\u0410\u0414 \u0421\u041e\u0424\u0422, 2012. \u2013 657 \u0441.<\/li>\n
  6. \u041a\u043b\u043e\u0432\u0430\u043d\u0438\u0447, \u0421. \u0424. \u041c\u0435\u0442\u043e\u0434 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u0432 \u0440\u0430\u0441\u0447\u0435\u0442\u0430\u0445 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0436\u0435\u043b\u0435\u0437\u043e\u0431\u0435\u0442\u043e\u043d\u043d\u044b\u0445 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0439 \/ \u0421. \u0424. \u041a\u043b\u043e\u0432\u0430\u043d\u0438\u0447, \u0414. \u0418. \u0411\u0435\u0437\u0443\u0448\u043a\u043e. \u2013 \u041e\u0434\u0435\u0441\u0441\u0430 : \u0418\u0437\u0434-\u0432\u043e \u041e\u041d\u041c\u0423, 2009. \u2013 89 \u0441.<\/li>\n
  7. Bagrii O. V. Plane problem of discrete environment mechanics. Problems of Tribology. 2022. \u2116 2. \u0420. 104\u2013111.<\/li>\n
  8. \u0411\u0443\u0433\u0440\u043e\u0432 \u0410. \u041a. \u0427\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u0434\u043b\u044f \u0433\u0440\u0443\u043d\u0442\u043e\u0432\u044b\u0445 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0439 \/ \u0410.\u00a0\u041a.\u00a0\u0411\u0443\u0433\u0440\u043e\u0432, \u041a. \u041a. \u0413\u0440\u0435\u0431\u043d\u0435\u0432 \/\/ \u041e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f, \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u044b \u0438 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0430 \u0433\u0440\u0443\u043d\u0442\u043e\u0432. \u2013 1977. \u2013 \u2116 3. \u2013 \u0421. 39\u201342.<\/li>\n
  9. \u0413\u043e\u043b\u044c\u0434\u0438\u043d \u0410. \u041b. \u041f\u043b\u043e\u0441\u043a\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0443\u043f\u0440\u0443\u0433\u043e\u0439 \u0433\u0440\u0443\u043d\u0442\u043e\u0432\u043e\u0439 \u0441\u0440\u0435\u0434\u044b \/ \u0410. \u041b. \u0413\u043e\u043b\u044c\u0434\u0438\u043d \/\/ \u0418\u0437\u0432\u0435\u0441\u0442\u0438\u044f \u0412\u041d\u0418\u0418\u0413. \u2013 1968. \u2013 \u0422. 87. \u2013 \u0421. 169\u2013174.<\/li>\n
  10. \u0417\u0430\u0440\u0435\u0446\u043a\u0438\u0439 \u042e. \u041a. \u0421\u0442\u0430\u0442\u0438\u043a\u0430 \u0438 \u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0430 \u0433\u0440\u0443\u043d\u0442\u043e\u0432\u044b\u0445 \u043f\u043b\u043e\u0442\u0438\u043d \/ \u042e. \u041a. \u0417\u0430\u0440\u0435\u0446\u043a\u0438\u0439, \u0412. \u041d. \u041b\u043e\u043c\u0431\u0430\u0440\u0434\u043e. \u2013 \u041c. : \u042d\u043d\u0435\u0440\u0433\u0438\u044f, 1983. \u2013 256 \u0441.<\/li>\n
  11. \u041a\u043e\u0432\u0442\u0443\u043d \u0412. \u0412. \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u044b\u0439 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0438 \u0433\u0440\u0443\u043d\u0442\u043e\u0432 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u042d\u0412\u041c \/ \u0412. \u0412. \u041a\u043e\u0432\u0442\u0443\u043d \/\/ \u0421\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0438 \u0433\u0440\u0443\u043d\u0442\u043e\u0432. \u2013 \u0427\u0435\u043b\u044f\u0431\u0438\u043d\u0441\u043a, 1985. \u2013 \u0421. 136\u2013137.<\/li>\n
  12. \u0421\u0430\u0445\u0430\u0440\u043e\u0432 \u0412. \u041e. \u041c\u043e\u0434\u0435\u043b\u044c \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0433\u043e \u0434\u0435\u0444\u043e\u0440\u043c\u0443\u0432\u0430\u043d\u043d\u044f \u0491\u0440\u0443\u043d\u0442\u043e\u0432\u043e\u0457 \u043e\u0441\u043d\u043e\u0432\u0438 \u0434\u043b\u044f \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0430\u043d\u043d\u044f \u0433\u0435\u043e\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u043f\u0440\u0438\u0431\u0443\u0434\u043e\u0432\u0438 \/ \u0412. \u041e. \u0421\u0430\u0445\u0430\u0440\u043e\u0432 \/\/ \u041e\u0441\u043d\u043e\u0432\u0438 \u0456 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0438 : \u043c\u0456\u0436\u0432\u0456\u0434. \u043d\u0430\u0443\u043a.-\u0442\u0435\u0445\u043d. \u0437\u0431. \u041a\u041d\u0423\u0411\u0410. \u2013 2005. \u2013 \u0412\u0438\u043f. 29. \u2013 \u0421. 8\u201319.<\/li>\n
  13. \u0413\u0440\u0438\u0448\u0438\u043d \u0412. \u0410. \u041d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0439, \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0445 \u0441 \u0433\u0440\u0443\u043d\u0442\u043e\u0432\u043e\u0439 \u0441\u0440\u0435\u0434\u043e\u0439 \/ \u0412. \u0410. \u0413\u0440\u0438\u0448\u0438\u043d, \u0412. \u0421. \u0414\u043e\u0440\u043e\u0444\u0435\u0435\u0432 \u2013 \u041e\u0434\u0435\u0441\u0441\u0430 : \u0412\u043d\u0435\u0448\u0440\u0435\u043a\u043b\u0430\u043c\u0441\u0435\u0440\u0432\u0438\u0441, 2006. \u2013 242 \u0441.<\/li>\n
  14. \u0411\u0430\u0433\u0440\u0456\u0439 \u041e. \u0412. \u0406\u0442\u0435\u0440\u0430\u0446\u0456\u0439\u043d\u0456 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u0440\u0456\u0448\u0435\u043d\u043d\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0457 \u0437\u0430\u0434\u0430\u0447\u0456 \u0434\u043b\u044f \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0430 \u0437 \u0441\u0443\u0442\u0442\u0454\u0432\u0438\u043c \u043f\u0440\u043e\u044f\u0432\u043e\u043c \u0432\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u044c\u043e\u0433\u043e \u0442\u0435\u0440\u0442\u044f \/ \u041e. \u0412. \u0411\u0430\u0433\u0440\u0456\u0439 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u2013 2022. \u2013 \u2116 4. \u2013 \u0421. 44\u201348.<\/li>\n<\/ol>\n

    References<\/em><\/strong><\/p>\n

      \n
    1. Prohramnyi kompleks SolidWorks. URL: https:\/\/www.solidworks.com\/<\/li>\n
    2. PLAXIS Geotechnical Analysis Software. URL: https:\/\/www.bentley.com\/en\/products\/brands\/plaxis<\/li>\n
    3. Avtomatyzovana systema naukovykh doslidzhen (ASND) \u00abVESNA\u00bb. URL: https:\/\/www.knuba.edu.ua\/ukr\/?page_id=934<\/li>\n
    4. Bahatofunktsionalnyi prohramnyi kompleks LIRA-SAPR. URL: https:\/\/www.liraland.ua\/lira\/<\/li>\n
    5. SCAD Office. Vychislitel’nyj kompleks SCAD \/ V. S. Karpilovskij, Je. Z. Kriksunov, A. A. Maljarenko, M. A. Mikitavrenko, A. V. Perel’muter, M. A. Perel’muter. \u2013 SKAD SOFT, 2012. \u2013 657 s.<\/li>\n
    6. Klovanich, S. F. Metod konechnyh jelementov v raschetah prostranstvennyh zhelezobetonnyh konstrukcij \/ S. F. Klovanich, D. I. Bezushko. \u2013 Odessa : Izd-vo ONMU, 2009. \u2013 89 s.<\/li>\n
    7. Bagrii O. V. Plane problem of discrete environment mechanics. Problems of Tribology. 2022. \u2116 2. R. 104\u2013111.<\/li>\n
    8. Bugrov A. K. Chislennoe reshenie fizicheski nelinejnyh zadach dlja gruntovyh osnovanij \/ A. K. Bugrov, K. K. Grebnev \/\/ Osnovanija, fundamenty i mehanika gruntov. \u2013 1977. \u2013 \u2116 3. \u2013 S. 39\u201342.<\/li>\n
    9. Gol’din A. L. Ploskaja zadacha fizicheski nelinejnoj uprugoj gruntovoj sredy \/ A. L. Gol’din \/\/ Izvestija VNIIG. \u2013 1968. \u2013 T. 87. \u2013 S. 169\u2013174.<\/li>\n
    10. Zareckij Ju. K. Statika i dinamika gruntovyh plotin \/ Ju. K. Zareckij, V. N. Lombardo. \u2013 M. : Jenergija, 1983. \u2013 256 s.<\/li>\n
    11. Kovtun V. V. Programmnyj kompleks dlja reshenija zadach nelinejnoj mehaniki gruntov s pomoshh’ju JeVM \/ V. V. Kovtun \/\/ Sovremennye problemy nelinejnoj mehaniki gruntov. \u2013 Cheljabinsk, 1985. \u2013 S. 136\u2013137.<\/li>\n
    12. Sakharov V. O. Model neliniinoho deformuvannia gruntovoi osnovy dlia rozviazannia heotekhnichnykh zadach prybudovy \/ V. O. Sakharov \/\/ Osnovy i fundamenty : mizhvid. nauk.-tekhn. zb. KNUBA. \u2013 2005. \u2013 Vyp. 29. \u2013 S. 8\u201319.<\/li>\n
    13. Grishin V. A. Nelinejnye modeli konstrukcij, vzaimodejstvujushhih s gruntovoj sredoj \/ V. A. Grishin, V. S. Dorofeev \u2013 Odessa : Vneshreklamservis, 2006. \u2013 242 s.<\/li>\n
    14. Bahrii O. V. Iteratsiini alhorytmy rishennia ploskoi zadachi dlia seredovyshcha z suttievym proiavom vnutrishnoho tertia \/ O. V. Bahrii \/\/ Herald of Khmelnytskyi National University. \u2013 2022. \u2013 \u2116 4. \u2013 S. 44\u201348<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[71],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/14796"}],"collection":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14796"}],"version-history":[{"count":5,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/14796\/revisions"}],"predecessor-version":[{"id":14991,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/14796\/revisions\/14991"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}