TAILIEUCHUNG - Phương pháp phần tử hữu hạn trong phân tích giới hạn đàn hồi - dẻo của một số bài toán cấu trúc
Phương pháp phần tử hữu hạn (FEM) được sử dụng rộng rãi trong phân tích elastoplastic hành vi cho cấu trúc. Phân tích thường liên quan đến quy trình hai giai đoạn: đầu tiên, trường nội lực tác dụng lên vật liệu kết cấu phải được xác định, và thứ hai, đáp ứng của vật liệu cho trường lực đó phải được xác định. | TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 9, SỐ 8 - 2006 FINITE ELEMENT ANALYSIS OF ELASTO-PLASTIC BOUNDARY FOR SOME STRUCTURE PROBLEMS Trương Tích Thiện (1), Cao Bá Hoàng (2) (1) Trường Đại học Bách Khoa, ĐHQG-HCM (2) Bộ Xây Dựng th st (Manuscript Received on January 26 , 2006, Manuscript Revised August 28 , 2006) ABSTRACT: The finite element method (FEM) is used widely in analysis of elastoplastic behaviours for structures. The analysis often involves a two-stage process: first, the internal force field acting on the structural material must be defined, and second, the response of the material to that force field must be determined. In other words, the analysis of behaviours of structural material is establishment relationships between stresses and strains in the structure in the plastic as well as elastic ranges. It furnishes more realistic estimates of load-carrying capacities of structures and provides a better understanding of the reaction of the structural elements to the forces induced in the material. Key words: Elasto-plastic, plasticity, Timoshenko, analysis 1. INTRODUCTION It is generally regarded that the origin of plasticity, as a branch of mechanics of continua, dated back to a series of papers from 1864 to 1872 by Tresca on the extrusion of metals, in which he proposed the first yield condition. The actual formulation of the theory was done in 1870 by St. Venant, who introduced the basic constitutive relations for what today we would call rigid, perfectly plastic materials in plane stress. A generalization similar to the results of Levy was arrived independently by von Mises in a landmark paper in 1913, accompanied by his well-known, pressure-insensitive yield criterion (J2-theory, or octahedral shear stress yield condition). In 1924, Prandtl extended the St. Venant-Levy-von Mises equations for the plane continuum problem to include the elastic component of strain, and Reuss in 1930 carried out their extension to three dimensions. The appropriate flow rule .
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