By Yu-Qiu Long, Song Cen, Zhi-Fei Long
Complex Finite point technique in Structural Engineering systematically introduces the learn paintings at the Finite point procedure (FEM), which used to be accomplished by way of Prof. Yu-qiu lengthy and his examine team long ago 25 years. Seven unique theoretical achievements - for example, the Generalized Conforming aspect procedure, to call one - and their purposes within the fields of structural engineering and computational mechanics are mentioned intimately. The booklet additionally indicates the recent concepts for fending 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 pressure suggestions through displacement-based components; tension singular element challenge) by using foregoing achievements.
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Example text
2-41) or the 3 2c( a ) in Eq. (2-65) will transform to the single-field complementary energy 3 1c( a ) : 3 1c( a ) wM ns · wM ns § § · ¨ Qn ws ¸ wds ³ C3 a ¨ Qn ws Vn ¸ wds © ¹ © ¹ a ww ³ M n\ n ds ³ (M n M n ) ds ¦ 'M ns w ¦ ('M ns R ) w C1a C2 a C3 a wn A1 a A2 a (2-70a) ³³: V ( M )dxdy ³ C1a C2 a ww can be looked upon as the Lagrange multipliers on the boundaries wn and their corner points. If M satisfies the traction boundary and corner point conditions in advance, then where w and 3 1c( a ) ³³: V ( M )dxdy ³ a C1a C2 a wM ns · § ¨ Qn ws ¸ wds ³ C1a M n\ n ds ¦ 'M ns w © ¹ A1a (2-70b) From Eqs.
The functional stationary condition G33p( a ) G33c(b ) GH pc G33 0 (2-5) is equivalent to the whole system of equations of the elastic body with subregions, including equilibrium differential equation: V ij , j Fi (in V) 0 (2-6) strain-displacement relations (geometrical equation) H ij 1 (ui , j u j ,i ) 2 (in V) (2-7) stress-strain relations (constitutive equation) V ij wU wH ij (in V) (2-8) boundary conditions of tractions Ti 18 V ij n j Ti (on SV) (2-9) Chapter 2 The Sub-Region Variational Principles boundary conditions of displacements ui ui (on Su) (2-10) and continuous conditions at the interface Ti ( a ) Ti (b ) ui( a ) ui(b ) (on Sab) (2-11) (on Sab) (2-12) In order to demonstrate the equivalency between the functional stationary condition (2-5) and the Eqs.
The key points of the sub-region three-field generalized variational principle (1) The field variables Both regions a and b possess three field variables: Deflections: w(a ) , w(b) Bending and twisting moments: M (a) [M x My M xy ]T( a ) M (b) [M x My M xy ]T( b ) Curvatures: ț (a) [N x N y 2N xy ]T( a ) ț (b) [N x N y 2N xy ]T(b ) These field variables are not required to satisfy any conditions in advance within the domain and on the boundaries and interfaces. (2) Definition of the functional Let the region a be the potential energy region, and the region b the complementary energy region.