Phương pháp Petrov-Galerkin địa phương không lưới cho các chất viscoelastic tuyến tính không đồng nhất liên tục

Computational Mechanics - Tập 37 - Trang 279-289 - 2005
J. Sladek1, V. Sladek1, Ch. Zhang2, M. Schanz3
1Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia
2Department of Civil Engineering, University of Siegen, Siegen, Germany
3Institute of Applied Mechanics, Graz University of Technology, Graz, Austria

Tóm tắt

Một phương pháp không lưới dựa trên cách tiếp cận Petrov-Galerkin địa phương được đề xuất để giải quyết các vấn đề tĩnh gần và động tạm thời trong môi trường viscoelastic tuyến tính không đồng nhất hai chiều (2-D). Một hàm bước đơn vị được sử dụng làm hàm kiểm tra trong dạng yếu địa phương. Phương pháp này dẫn đến các phương trình tích phân biên cục bộ (LBIEs) chỉ liên quan đến một tích phân miền trong trường hợp các vấn đề động tạm thời. Nguyên tắc ứng xử tương ứng được áp dụng cho các chất rắn viscoelastic không đồng nhất như vậy, trong đó các mô-đun thả lỏng có thể tách rời theo các biến không gian và thời gian. Sau đó, các LBIEs được hình thành cho vấn đề viscoelastic được biến đổi Laplace. Miền được phân tích được bao phủ bởi các miền con nhỏ với hình dạng đơn giản như các hình tròn trong các vấn đề 2-D. Phương pháp bình phương tối thiểu dịch chuyển (MLS) được sử dụng để xấp xỉ các đại lượng vật lý trong các LBIEs.

Từ khóa

#Phương pháp không lưới #Petrov-Galerkin #viscoelastic tuyến tính #phương trình tích phân biên cục bộ #phương pháp bình phương tối thiểu dịch chuyển

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