tailieunhanh - dohrmann Episode 2 Part 5

Tham khảo tài liệu 'dohrmann episode 2 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | where 0 1 1. The bounding values of 2 which define Fge are determined from the projections described previously. It follows from Eqs. 29-33 that XjnrjdS í ỘMtjkmXkẠXm ì - for j 1 2 3 34 0XjM JFge J JAfr 33- i XjTtdS í ộse jkmXk iXm idA for j 1 2 3 35 dxjS JFge J JAir where Acr is the area of integration for Fge in the i- 2 coordinate system and Xịsộse XìmỘm i Ỉ 1 2 a2 2 36 XiMKdỘM ỠTÌ bỵ dỘM dm ỵi- Xisidộse d i 37 The integrals on the right hand sides of Eqs. 34-35 can be calculated exactly using a 2-point Gauss quadrature rule in the 1 direction. For edges on the slave surface with three or fewer nodes the following quadrature rules for the 2 direction are sufficient 3-point for a 4-node tetrahedron or 8-node hexahedron with a face on the master surface 4-point for a 6-node tetrahedron or a 20-node hexahedron and 6-point for a 27-node hexahedron. The surface integrals in Eq. 24 over the domain Fr are obtained from Eqs. 34-35 by summing the contributions from all involved segments on the master surface. If the slave surface consists entirely of uniform strain elements then all the necessary corrections are contained in Bjj. By using Eqs. 24 to calculate for elements with faces on the slave surface one can perform analyses of connected meshes for both linear and nonlinear problems. A general method of hourglass control 10 can also be used to stabilize any elements on the boundary with spurious zero energy deformation modes. The remainder of this section is concerned with extending the method to accommodate more commonly used finite elements on the slave surface. Although we believe the method can be extended easily to nonlinear problems attention is restricted presently to the linear case. Needless to say many problems of practical interest are in this category. Prior to any modifications the stiffness matrix K of an element with a face on the slave surface can be expressed as K Ku Kr 38 where Ku denotes the uniform strain portion of K and Kr is the .

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