Математичне моделювання і аналіз напруженого стану в ортотропному п’єзоелектричному середовищі з круговою тріщиною

• Date: 2017
• Author Affiliations: Vitaliy Kirilyuk — Отдел механики стохастически-неоднородных сред Института механики имени С.П.Тимошенко НАНУ, Киев; Olga Levchuk — Отдел механики стохастически-неоднородных сред Института механики имени С.П.Тимошенко НАНУ, Киев; Olena Gavrilenko — Факультет информатики и вычислительной техники Национального технического университета Украины "Киевский политехнический институт имени Игоря Сикорского", Киев
• Keywords: keywords
• Main Authors: Kirilyuk, Vitaliy, Levchuk, Olga, Gavrilenko, Olena
• Format: Article
• Language: Russian
• Published: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2017
• Subjects: математичне моделювання; зв’язана система рівнянь електропружності; ортотропний п’єзоелектричний матеріал; плоска кругова тріщина; однорідні навантаження; коефіцієнти інтенсивності напружень
• Online Access: https://journal.iasa.kpi.ua/article/view/106880
• Journal Title: System research and information technologies

A mathematical model for the analysis of the stress state in an orthotropic electroelastic material with a circular (penny-shaped) crack is developed. The model is based on the consideration of the coupled system of electroelasticity equations. The problem on electric and stress states in orthotropic piezoelectric space with an elliptical crack under the force and electric loading was considered. The solution of the problem was obtained by means of using of the triple Fourier transform and Fourier image of Green's function for an infinite orthotropic piezoelectric medium. The approach was tested in the case of the location crack in the isotropy plane of transversely isotropic piezoelectric material for which there was an exact solution of the problem. The comparison of the calculated results confirmed the high efficiency of the used approach. Numerical experiments were conducted and distributions of stress intensity factors along elliptical crack front in orthotropic piezoelectric materials and elastic orthotropic materials under uniform force loading were investigated.