Phân tích vỡ của các vết nứt trong các vật thể từ điện đàn hồi bằng phương pháp MLPG

Computational Mechanics - Tập 42 - Trang 697-714 - 2008
J. Sladek1, V. Sladek1, P. Solek2, E. Pan3
1Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia
2Department of Mechanics, Slovak Technical University, Bratislava, Slovakia
3Computer Modeling and Simulation Group, Department of Civil Engineering, University of Akron, Akron, USA

Tóm tắt

Một phương pháp không lưới dựa trên cách tiếp cận Petrov-Galerkin địa phương được đề xuất để phân tích vết nứt trong các vật thể từ điện đàn hồi đối xứng trục hai chiều (2-D) và ba chiều (3-D) với các tính chất vật liệu liên tục biến đổi. Đối xứng trục của hình dạng và các điều kiện biên làm giảm bài toán giá trị biên 3-D ban đầu thành bài toán 2-D trong mặt cắt ngang trục. Các vấn đề động lực học tĩnh và tạm thời được xem xét trong bài báo này. Phương pháp yếu địa phương được áp dụng trên các miền con hình tròn, nơi các nút xung quanh được phân bố ngẫu nhiên trên miền phân tích. Các hàm kiểm tra được lấy dưới dạng các hàm bước đơn vị trong quá trình suy diễn các phương trình tích phân địa phương (LIEs). Phương pháp bình phương tối thiểu dịch chuyển (MLS) được áp dụng để gần đúng các đại lượng vật lý trong các LIEs. Độ chính xác của phương pháp hiện tại trong việc tính toán các hệ số cường độ ứng suất (SIF), các hệ số cường độ dịch chuyển điện (EDIF) và các hệ số cường độ cảm ứng từ (MIIF) được thảo luận thông qua sự so sánh với các giải pháp số cho các vật liệu đồng nhất.

Từ khóa

#phương pháp không lưới #phân tích vết nứt #vật thể từ điện đàn hồi #phương pháp Petrov-Galerkin #phương pháp bình phương tối thiểu dịch chuyển.

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