By Josep M. Font-Llagunes (eds.)
This e-book comprises chosen papers from the ECCOMAS Thematic convention on Multibody Dynamics, that came about in Barcelona, Spain, from June 29 to July 2, 2015. through having its beginning in analytical and continuum mechanics, in addition to in machine technology and utilized arithmetic, multibody dynamics offers a foundation for research and digital prototyping of cutting edge functions in lots of fields of latest engineering. With the usage of computational types and algorithms that classically belonged to varied fields of utilized technological know-how, multibody dynamics can provide trustworthy simulation systems for various highly-developed commercial items comparable to car and railway platforms, aeronautical and house automobiles, robot manipulators, clever constructions, biomechanical structures, and nanotechnologies.
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Extra info for Multibody Dynamics: Computational Methods and Applications
48) where F ∗0 = F ∗ (0, 0) and matrix G is given in Eqs. 69). This solution corresponds to the case where the in-plane shearing and twisting resultants are constant, while extension, transverse shearing, and bending resultants are cosine and sine waves in the shell’s midplane surface. 44) now becomes Y = I G F ∗0 , where matrix I = [0 N ×3n , I N ×N ]T . The particular solution has a similar form, X = X F ∗ = E E E X G F ∗0 , where matrix X T = [W T , S T ] stores the warping, W , and strain measures, S, induced by unit stress resultants, respectively.
3 The Deformed Configuration The displacement field of the material line has been decomposed into two parts: the rigid-normal motion and an arbitrary warping field, denoted u(η1 , η2 , η3 ), which describes the displacement of material point P with respect to point PR , see Fig. 1. Because the warping field is arbitrary, it also includes a rigid-body motion, and hence, rigid-body motions are double counted. This ambiguity of the formulation will be resolved later, based on physical arguments. In the deformed configuration, 3 Three-Dimensional Non-linear Shell Theory for Flexible Multibody Dynamics 41 the position vector of a material point becomes r P (η1 , η2 , η3 ) = r PR (η1 , η2 , η3 ) + (R R 0 )u ∗ .
44) is a hybrid system that combines the local equilibrium equations expressed in terms the warping field with the global constitutive equation written in terms stress resultants and strain measures. These combined equations plays a central role because they link the local and global problems in a formal manner. These combined equations are solved in both the dimensional reduction and stress recovery processes. 44) features N T = 3n + NE unknowns, where NE is the number of independent strain measures, see Eq.