By Yu-Qiu Long, Song Cen, Zhi-Fei Long
Complicated Finite aspect process in Structural Engineering systematically introduces the learn paintings at the Finite point technique (FEM), which used to be accomplished by way of Prof. Yu-qiu lengthy and his examine team some time past 25 years. Seven unique theoretical achievements - for example, the Generalized Conforming point process, to call one - and their purposes within the fields of structural engineering and computational mechanics are mentioned intimately. The ebook additionally exhibits the recent 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 parts; accuracy loss challenge of pressure options by means of displacement-based parts; pressure singular aspect challenge) by using foregoing achievements.
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Extra info for Advanced Finite Element Method in Structural Engineering
2-21), and ui( a ) or ui( b ) in Eq. (2-23), can be treated as Lagrange multipliers. 5 The General Form of the Multi-Region Variational Principle for Elasticity From the above discussions, a general form of the multi-region variational principle can be obtained. Let an elastic body be divided into several sub-regions (see Fig. 2). Each subregion can be arbitrarily appointed as potential energy region or complementary energy region, and each region can be three-field region, or two-field region or single-field region.
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. The subregion single-field, two-field, three-field and their mixed forms are all special cases of the general form. (3) The displacement and traction conditions on each interface can be relaxed partly or completely.
2-42); The fourth term denotes the sum of the additional potential energy term Hpp on the interface Cpp, in which Hpp is given by Eq. (2-56); The fifth term denotes the sum of the additional complementary energy term Hcc on the interface Ccc, in which Hcc is given by Eq. (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.