Phân tích phi tuyến tĩnh dầm có cơ tính biến thiên hai chiều trên nền đàn hồi=Nonlinear static analysis of bidirectional functionally graded beams on an elastic foundation

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Tác giả: Văn Chình Nguyễn

Ngôn ngữ: vie

Ký hiệu phân loại:

Thông tin xuất bản: Tạp chí Khoa học công nghệ xây dựng (Đại học Xây dựng Hà Nội), 2024

Mô tả vật lý: tr.138-152

Bộ sưu tập: Metadata

ID: 237880

Thêm vào giỏ

Bài báo này tập trung phân tích ứng xử phi tuyến tĩnh của dầm có cơ tính biến đổi theo hai phương (2D-FG), đặt trên nền đàn hồi và chịu tác dụng của lực phân bố đều hoặc phân bố dạng hình sin bằng phương pháp phần tử hữu hạn. Vật liệu dầm bao gồm hai thành phần chính là gốm và kim loại, với các đặc trưng cơ học biến đổi liên tục theo chiều cao và chiều dài của dầm. Quan hệ giữa biến dạng và chuyển vị được xây dựng dựa trên lý thuyết biến dạng trượt bậc cao với ba ẩn chuyển vị, có kể đến phi tuyến hình học Von Kármán. Quan hệ giữa ứng suất và biến dạng tuân theo định luật Hooke. Phần tử dầm hai điểm nút với các hàm nội suy tuyến tính và bậc ba được sử dụng để rời rạc và xây dựng hệ phương trình cân bằng tĩnh phi tuyến cho dầm. Hệ phương trình cân bằng phi tuyến tĩnh được giải trên cơ sở phương pháp lặp Newton–Raphson. Độ tin cậy của mô hình được kiểm chứng qua kết quả so sánh với các tác giả đã công bố. Ảnh hưởng của một số yếu tố hình học, vật liệu và điều kiện biên đến độ võng của dầm được khảo sát và thảo luận chi tiết.This paper focuses on analyzing the nonlinear static behavior of beams with mechanical properties varying in two directions (2D-FG), resting on an elastic foundation and subjected to uniform distributed or sinusoidally distributed forces by finite element method. Beam materials include two components, ceramic and metal, with mechanical properties that continuously change according to the thickness and length directions of the beam. The relationship between deformation and displacement is built based on the theory of high-order shear deformation with three unknown displacements, and includes Von Kármán geometric nonlinearity. The relationship between stress and strain obeys Hooke’s law. Two-nodal beam elements with linear and cubic interpolation functions are used to discretize the domain and establish static nonlinear equilibrium equations for the beam. The nonlinear equilibrium equations are solved by using the Newton–Raphson iterative method. The reliability of the model is verified through comparison results with data in literature. The influences of geometric parameters, materials parameters and boundary conditions on the deflection of beams are investigated and discussed in detail.

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