By Yu-Qiu Long, Song Cen, Zhi-Fei Long
Complex Finite aspect technique in Structural Engineering systematically introduces the study paintings at the Finite aspect process (FEM), which was once accomplished through Prof. Yu-qiu lengthy and his learn workforce long ago 25 years. Seven unique theoretical achievements - for example, the Generalized Conforming point approach, to call one - and their purposes within the fields of structural engineering and computational mechanics are mentioned intimately. The booklet additionally exhibits the hot ideas for keeping off 5 problems that exist in conventional FEM (shear-locking challenge of thick plate parts; sensitivity challenge to mesh distortion; non-convergence challenge of non-conforming components; accuracy loss challenge of pressure ideas by way of displacement-based components; pressure singular aspect challenge) by using foregoing achievements.
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Extra resources for Advanced Finite Element Method in Structural Engineering
2-60). The sixth term denotes the sum of the additional energy term G1 at the node J1 (where the displacement is specified) of the adjacent sub-regions, in which G1 ¦ ('M ns ) ep 38 ( ep ) (w ( ep ) w) ¦ ('M ns )( ec ) w ec (2-75) Chapter 2 The Sub-Region Variational Principles The first term on the right side of the above equation means the sum of all the potential elements ep around the node; the second term means the sum of all the complementary energy elements ec around the node. The seventh term denotes the sum of the additional energy term G2 at the node J2 (where the concentrated force is specified) of the adjacent sub-regions, in which G2 [¦ ('M ns )( e ) R ]w( a ) ¦ ('M ns ) e The ( ep ) w ( ep ) (2-76) ep ¦ in the first term on the right side of the above equation denotes the sum e of all the elements e (including all ep and ec) around the node; w( a ) is the displacement of any element a around the node; The ¦ in the second term on ep the right side of the above equation denotes the sum of all the potential elements ep around the node.
In the sub-region generalized variational principle for shallow shell, the mid and the bottom surfaces of the shallow shell are divided into several sub-regions. Each sub-region can be arbitrarily appointed as single-field, two-field and three-field potential energy regions (such as : p1, : p2 and : p3 in Fig. 8), or the complementary energy regions (such as : c1, : c2 and : c3 in Fig. 8). The interfaces between two adjacent sub-regions are of three types, Cpc, Cpp and Ccc (Fig.
Compared with the thin plate theory, the characteristics of the thick plate theory are as follows: the influences of the transverse shear strain Jx and Jy (abbreviations of Jxz and Jyz) are considered; the rotations \x and \y are not dependent on the deflection w , thereby, w, \x and \y are three independent displacements; Besides the normal load q , there still are couple loads mx and my ; the transverse shear forces Qx and Qy are not dependent on the bending and twisting moments Mx, My and Mxy.
Advanced Finite Element Method in Structural Engineering by Yu-Qiu Long, Song Cen, Zhi-Fei Long