土建外文翻譯----剪力墻框架結構中的應力分布

1、附錄英文原文及翻譯Stress Distribution In a Shear Wall – Frame StructureUsing Unstructured – Refined Finite Element MeshABSTRACTA semi-automatic algorithm for finite element analysis is presented to obtain the stress and strain di

2、stribution in shear wall-frame structures. In the study, a constant strain triangle with six degrees of freedom and mesh refinement - coarsening algorithms were used in Matlab® environment. Initially the proposed al

3、gorithm generates a coarse mesh automatically for the whole domain and the user refines this finite element mesh at required regions. These regions are mostly the regions of geometric discontinuities. Deformation, normal

4、 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, Unstructured

5、 mesh, Refinement.1.INTRODUCTIONIn 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

6、placed in building plans reducing lateral displacements under earthquake loads so shear-wall frame structures are obtained. Since the 1960’s several approaches have been adopted to solve displacements and stress distribu

7、tion of shear wall structures. Continuous medium approaches, and frame analogy models are the examples of these approaches [1-4]. In the past and today, numerical solution methodsare the main effort area because of the a

8、ccuracy 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

9、 is uniformly 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

10、as triangles or quadrilaterals (in 2D) are called elements. The connection of these individual elements at nodes and along interelement boundaries covering the whole problem domain is called finite element mesh or grid.

11、In the literature meshes can be grouped into two main categories such as structured Figure 2. Constant strain triangular finite elementCST element has displacement functions and shape functions as follows,（1） ? ?? ? 3 3

12、2 2 1 13 3 2 2 1 1,,v N v N v N y x vu N u N u N y x u? ? ?? ? ?（2） ? ? ? ? ? ? ? ? ? ? y x x x y y y x y x A y x Ne2 3 2 3 2 3 3 2 1 21 , ? ? ? ? ? ?（3） ? ? ? ? ? ? ? ? ? ? y x x x y y y x y x A y x Ne3 1 3 1 3 1 1 3 2

13、21 , ? ? ? ? ? ?（4） ? ? ? ? ? ? ? ? ? ? y x x x y y y x y x A y x Ne1 2 1 2 1 2 2 1 3 21 , ? ? ? ? ? ?where 1 u , 2 u and 3 u nodal displacements in x direction corresponding to nodes 1, 2 and 3 respectively. 1 v , 2 v a

14、nd 3 v nodal displacements in y direction and 1 N , 2 N and 3 N are linear shape functions. x and y are the coordinates of corresponding nodes and e A is area of the element. In the finite element method, nodal displacem

15、ents are obtained from the solution of the linear system of equations, that is（5） f Ku ?where, K is stiffness matrix, u is nodal displacement vector, and f is nodal load vector. Stiffness matrix may be calculated as（6） ?

16、 ? ? ? SN C SN t A KTe ?where t is thickness of the element,（7） ? ??? ?? ?3 2 13 2 10 0 00 0 0N N NN N N Nand differential operator is,（8）? ? ? ???? ? ? ????????????x yy x S00and the elasticity matris is defined by（9）? ?