ranh giới phần tử (nút) điều kiện, phương trình 5,18, hệt hài lòng. Thay thế của các giải pháp giả định vào phương trình 5,19 cung cấp cho người còn lại lànơi superscript là một lần nữa được sử dụng để chỉ ra rằng còn lại là cho các phần tử. Áp dụng tiêu chuẩn Galerkin trọng còn lại | I Text Hutton Fundamentals of Finite Element Analysis 6. Interpolation Functions for General Element Formulation The McGraw-Hill Companies 2004 194 CHAPTER 6 Interpolation Functions for General Element Formulation Figure a A domain to be modeled. b Triangular elements. c Rectangular elements. d Rectangular and quadrilateral elements. closer to the actual geometry. However also note that the elements in the inner rows become increasingly slender . the height to base ratio is large . In general the ratio of the largest characteristic dimension of an element to the smallest characteristic dimension is known as the aspect ratio. Large aspect ratios increase the inaccuracy of the finite element representation and have a detrimental effect on convergence of finite element solutions 8 . An aspect ratio of 1 is ideal but cannot always be maintained. Commercial finite element software packages provide warnings when an element s aspect ratio exceeds some predetermined limit. In Figure to maintain a reasonable aspect ratio for the inner elements it would be necessary to reduce the height of each row of elements as the center of the sector is approached. This observation is also in keeping with the convergence requirements of the -refinement method. Although the triangular element can be used to closely approximate a curved boundary other considerations dictate a relatively large number of elements and associated computation time. If we consider rectangular elements as in Figure an intentionally crude mesh for illustrative purposes the problems are apparent. Unless the elements are very small the area of the domain excluded from the model the I Text Hutton Fundamentals of Finite Element Analysis 6. Interpolation Functions for General Element Formulation The McGraw-Hill Companies 2004 Isoparametric Formulation 195 shaded area in the figure may be significant. For the case depicted a large number of very small square elements best approximates the .
