Nghiên cứu nội lực và chuyển vị của dầm bằng phương pháp sai phân hữu hạn=Study of internal forces and displacements of beams by finite difference method

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Tác giả: Văn Duẩn Đoàn

Ngôn ngữ: vie

Ký hiệu phân loại:

Thông tin xuất bản: Tạp chí Xây dựng, 2024

Mô tả vật lý: tr.119

Bộ sưu tập: Metadata

ID: 478692

Thêm vào giỏ

In classical structural mechanics the main goal is to find continuous solutions, which is possible only for a very limited number of problems. Therefore, for each problem a separate method is applied to find its own solution. In contrast to the methods of classical structural mechanics, the application of a number of numerical methods according to a relatively unified scheme leads to universal electronic computer programs. The finite difference method is one of the two basic numerical methods along with the finite element method that is currently the most widely used, without question, for engineering problems in general and structural engineering problems in particular. The finite difference method solves most structural mechanics problems by solving differential equations or systems of differential equations. The exact solutions of these equations can be determined for some simple special cases with physical characteristics and pre-selected boundary conditions of the structure. In practice, applications are very diverse, and exact solutions in explicit form for most structural problems do not exist. Numerical methods then create rich possibilities for finding solutions. The difference method is a classical form in this direction. Keywords: Finite difference method
internal forces and displacements of beams.Trong cơ học kết cấu cổ điển mục đích chính là đi tìm các nghiệm liên tục, mà điều đó chỉ có thể thực hiện đối với một số rất hạn chế các bài toán. Do vậy, với mỗi bài toán lại vận dụng một phương pháp riêng để tìm lời giải cho chính nó. Khác với các phương pháp của cơ học kết cấu cổ điển, sự vận dụng một số loại phương pháp số theo một sơ đồ tương đối thống nhất dẫn đến các chương trình tính bằng máy tính điện tử với tính chất vạn năng [4]. Phương pháp sai phân hữu hạn là một trong hai phương pháp số cơ bản cùng với phương pháp phần tử hữu hạn mà ngày nay đang dùng phổ biến nhất không cần bàn cãi đối với các bài toán kỹ thuật nói chung và bài toán kết cấu công trình nói riêng. Phương pháp sai phân hữu hạn giải hầu hết các bài toán cơ học kết cấu đều đưa về giải phương trình vi phân hoặc hệ phương trình vi phân. Nghiệm chính xác của các phương trình này có thể xác định được cho một số trường hợp riêng đơn giản với các đặc trưng vật lý và các điều kiện biên chọn trước của kết cấu. Thực tế ứng dụng rất đa dạng, mà nghiệm chính xác dưới dạng tường minh của phần lớn các bài toán kết cấu không có. Khi đó các phương pháp số tạo ra khả năng phong phú để tìm lời giải. Phương pháp sai phân là một dạng cổ điển theo hướng này [4, 7]. Từ khóa: Sai phân hữu hạn
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