土建外文翻译----剪力墙框架结构中的应力分布

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1、PDF外文：http:/  英文原文及翻译  Stress Distribution In a Shear Wall Frame Structure Using Unstructured Refined Finite Element Mesh ABSTRACT A semi-automatic algorithm for finite element analysis is presented to obtain the stress and strain distribution in shear wall-frame structures. In the study,

2、a constant strain triangle with six degrees of freedom and mesh refinement - coarsening algorithms were used in Matlab environment. Initially the proposed algorithm generates a coarse mesh automatically for the whole domain and the user refines this finite element mesh at required regions. These reg

3、ions are mostly the regions of geometric discontinuities. Deformation, normal and shear stresses are presented for an illustrative example. Consistent displacement and stress results have been obtained from comparisons with widely used engineering software.  Key Words: Shear wall, FEM, Unstruct

4、ured mesh, Refinement.  1.INTRODUCTION In the last two decades, shear walls became an important part of our mid and high rise residential buildings in Turkey. As part of an earthquake resistant building design, these walls are placed in building plans reducing lateral displacements under earthq

5、uake loads so shear-wall frame structures are obtained. Since the 1960s several approaches have been adopted to solve displacements and stress distribution of shear wall structures. Continuous medium approaches, and frame analogy models are the examples of these approaches 1-4. In the past and today

6、, numerical solution methods are the main effort area because of the accuracy of solution and the ease of usage in 2D and 3D analysis of shear walls 5-7.  Shear walls with openings, coupled shear walls and combined shear wall frame structures can be modeled as thin plates where the loading is u

7、niformly distributed over the thickness, in the plane of the plate. This 2D domain can be subdivided into a finite number of geometrical shapes. In the finite element method (FEM), these simple shaped elements such as triangles or quadrilaterals (in 2D) are called elements. The connection of these i

8、ndividual elements at nodes and along interelement boundaries covering the whole problem domain is called finite element mesh or grid. In the literature meshes can be grouped into two main categories such as structured and unstructured meshes. Structured meshes are constructed with geometrically sim

9、ilar triangular or quadrilateral elements. They are suitable especially for problems with simple geometry and boundary shapes (Figure 1-a). Although structured meshes can be constructed as simple-time saving routines, regarding complicated domains with complex boundaries, it is a problem to fit the

10、boundary shape. To circumvent this difficulty, unstructured meshes are used to discretize the complicated domains with internal boundaries (Figure 1-b). While it is a time consuming procedure, unstructured meshes are also suitable for local mesh refinement and coarsening. The aim of this work is to

11、get a good quality unstructured mesh which will have smaller elements at the geometric discontinuities and bigger elements at other regions for a shear wall frame geometry.  Figure 1. Structured (a) and unstructured mesh (b)  2. TRIANGULAR FINITE ELEMENTS 2.1. Element Formulation The first

12、 advantage of using triangular elements is that almost any plane geometry may be discretized using triangles. These elements have six degrees of freedom, two translations at each node (Figure 2). Because of the three nodes, the element has linear shape functions that are an additional benefit becaus

13、e of simplified mathematics. However, these functions generate constant strain and stress throughout the element. To surmount this disadvantage, smaller elements must be employed where strain and stress vary rapidly.   Figure 2. Constant strain triangular finite element  CST element has di

14、splacement functions and shape functions as follows, 332211332211, vNvNvNyxv uNuNuNyxu  （ 1）   yxxxyyyxyxAyxNe 232323321 21,  （ 2）   yxxxyyyxyxAyxNe 313131132 21,  （ 3）   yxxxyyyxyxAyxNe 121212213 21,  （ 4）  where 1 u , 2 u and 3 u nodal displacements in x dir

15、ection corresponding to nodes 1, 2 and 3 respectively. 1 v , 2 v and 3 v nodal displacements in y direction and 1 N , 2 N and 3 N are linear shape functions. xand y are the coordinates of corresponding nodes and e A is area of the element. In the finite element method, nodal displacements are obtain

16、ed from the solution of the linear system of equations, that is fKu （ 5）  where, K is stiffness matrix, u is nodal displacement vector, and f is nodal load vector. Stiffness matrix may be calculated as SNCSNtAK Te  （ 6）  wheret is thickness of the element, 321 321 000 000 NNN NNNN  （ 7）  and differential operator is, xyyxS00 （ 8）  and the elasticity matris is defined by 210001011 2 vvvEC （ 9）