By Yu-Qiu Long, Song Cen, Zhi-Fei Long
Complicated Finite aspect procedure in Structural Engineering systematically introduces the learn paintings at the Finite aspect technique (FEM), which used to be accomplished through Prof. Yu-qiu lengthy and his study workforce long ago 25 years. Seven unique theoretical achievements - for example, the Generalized Conforming point technique, to call one - and their purposes within the fields of structural engineering and computational mechanics are mentioned intimately. The publication additionally indicates the hot thoughts for warding off 5 problems that exist in conventional FEM (shear-locking challenge of thick plate components; sensitivity challenge to mesh distortion; non-convergence challenge of non-conforming components; accuracy loss challenge of tension recommendations by means of displacement-based parts; rigidity singular aspect challenge) by using foregoing achievements.
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The fifth term denotes the sum of the additional term Hcc on the interface Scc, in which Hcc is given by Eq. (2-23). It can be shown that the stationary condition G3 0 25 Advanced Finite Element Method in Structural Engineering of the functional 3 in Eq. (2-35) is equivalent to all equations, boundary conditions and interface continuous conditions of the elastic body with multi-regions. If all regions are potential energy regions, the functional of the sub-region potential (or generalized potential) energy principle can be obtained from Eq.
2-23b). 6 Some Remarks The general form of the sub-region generalized variational principle for small displacement elasticity problems is presented in this section, and Eq. (2-35) is its functional expression. Its universality is due to the following reasons: (1) Each sub-region can be independently specified as potential and complementary energy regions, and the sub-region potential energy, complementary energy and mixed variational principle are three special forms of the general form. (2) The field variables in each region can be specified independently.
There are also three independent internal moment components Mx, My and Mxy, and their corresponding generalized strains are the curvature variety values Nx, Ny and Nxy. Furthermore, the transverse shear forces Qx and Qy are dependent internal force components, and can be determined by Mx, My and Mxy. In thin shells, the transverse shear strain Jxz and Jyz are both zero. On the boundary line C of the shallow shell, let n and s be the outer normal and the tangent directions. The displacement components along n, s and ] directions of an arbitrary point on the boundary line are un, vs and wˈand the corresponding boundary forces are normal tension Nn, tangent shear force Nns, wM ns and equivalent transverse shear force Vn Qn which is synthesized by ws 51 Advanced Finite Element Method in Structural Engineering the transverse shear force Qn and the twisting moment Mns.