Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses

Bobonazarov, Akmal, Khaldjigitov, Abduvali, Tilovov, Otajon, Бобоназаров, Акмал, Халджигитов, Абдували, Тиловов, Отажон, Bobonazarov, Akmal, Xaldjigitov, Abduvali, Tilovov, Otajon

Mexanika muammolari jurnali · 2026-yil

Annotatsiya

This study addresses the formulation and numerical solution of a plane dynamic elasticity problem in which the stress tensor components are the primary unknowns. The objective is to develop a numerical algorithm for directly determining the dynamic stress field in a homogeneous isotropic elastic medium. The equations of motion, strain--displacement relations, and Hooke's law are used to derive a system of three differential equations in terms of stresses, supplemented by initial and boundary conditions. Spatial discretization is performed using the Galerkin finite element method. Time integration is carried out using the Newmark method in a C++ program and a finite difference scheme in a FreeFEM++ implementation. A rectangular domain is subjected to a time-dependent normal load on its upper boundary, while the remaining boundaries are traction-free. Spatial stress distributions and the time history of the normal stress at the centre of the domain are obtained. Comparison of the two implementations shows qualitative agreement in the stress distributions and their oscillatory behaviour. The results demonstrate the applicability of the approach to the numerical investigation of plane dynamic elasticity problems formulated in terms of stresses.

Maqola ma’lumotlari
MualliflarBobonazarov, Akmal, Khaldjigitov, Abduvali, Tilovov, Otajon, Бобоназаров, Акмал, Халджигитов, Абдували, Тиловов, Отажон, Bobonazarov, Akmal, Xaldjigitov, Abduvali, Tilovov, Otajon
JurnalMexanika muammolari jurnali
NashriyotМеханика ва иншоотлар сейсмик мустаҳкамлиги институти
ISSN2010-7250
Nashr sanasi2026-09-30
Jild37
Son3
TilIngliz
Indeksga qo‘shilgan2026-10-18

Maqolaning asl sahifasi

Kalit so‘zlar

dynamic elasticity, stress formulation, finite element method, Galerkin method, Newmark method, finite difference scheme, FreeFEM++, динамическая упругость, формулировка в напряжениях, метод конечных элементов, метод Галёркина, метод Ньюмарка, конечно-разностная схема, FreeFEM++, dinamik elastiklik, kuchlanishlar orqali ifodalash, chekli elementlar usuli, Galerkin usuli, Newmark usuli, chekli ayirmalar sxemasi, FreeFEM++

Iqtibos keltirish

APABobonazarov, Akmal, Khaldjigitov, Abduvali, Tilovov, Otajon, Бобоназаров, Акмал, Халджигитов, Абдували, Тиловов, Отажон, Bobonazarov, Akmal, Xaldjigitov, Abduvali, & Tilovov, Otajon (2026). Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses. Mexanika muammolari jurnali, 37(3). https://www.pmjournal.uz/index/article/view/20
GOST (OAK)Bobonazarov, Akmal va b. Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses // Mexanika muammolari jurnali. – 2026. – T. 37, № 3.
MLABobonazarov, Akmal, Khaldjigitov, Abduvali, Tilovov, Otajon, Бобоназаров, Акмал, Халджигитов, Абдували, Тиловов, Отажон, Bobonazarov, Akmal, Xaldjigitov, Abduvali, and Tilovov, Otajon. “Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses.” Mexanika muammolari jurnali, 37(3), 2026. https://www.pmjournal.uz/index/article/view/20
ChicagoBobonazarov, Akmal, Khaldjigitov, Abduvali, Tilovov, Otajon, Бобоназаров, Акмал, Халджигитов, Абдували, Тиловов, Отажон, Bobonazarov, Akmal, Xaldjigitov, Abduvali, and Tilovov, Otajon. “Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses.” Mexanika muammolari jurnali, 37(3) (2026). https://www.pmjournal.uz/index/article/view/20
HarvardBobonazarov, Akmal, Khaldjigitov, Abduvali, Tilovov, Otajon, Бобоназаров, Акмал, Халджигитов, Абдували, Тиловов, Отажон, Bobonazarov, Akmal, Xaldjigitov, Abduvali, and Tilovov, Otajon (2026) ‘Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses’, Mexanika muammolari jurnali, 37(3). https://www.pmjournal.uz/index/article/view/20
BibTeX
@article{bobonazarovakmal2026,
  title = {Numerical Solution of the Plane Dynamic Problem of Elasticity in Terms of Stresses},
  author = {Bobonazarov, Akmal and Khaldjigitov, Abduvali and Tilovov, Otajon and Бобоназаров, Акмал and Халджигитов, Абдували and Тиловов, Отажон and Bobonazarov, Akmal and Xaldjigitov, Abduvali and Tilovov, Otajon},
  journal = {Mexanika muammolari jurnali},
  year = {2026},
  volume = {37},
  number = {3},
  url = {https://www.pmjournal.uz/index/article/view/20}
}

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