A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

A new 3-node triangular hybrid displacement function Mindlin- Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses

Computational Static Aeroelasticity Using Nonlinear Structures and Aerodynamics Models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106442/1/AIAA2013-1862.pd

Electronic Structures of Quantum Dots and the Ultimate Resolution of Integers

The orbital angular momentum L as an integer can be ultimately factorized as a product of prime numbers. We show here a close relation between the resolution of L and the classification of quantum states of an N-electron 2-dimensional system. In this scheme, the states are in essence classified into different types according to the m(k)-accessibility, namely the ability to get access to symmetric geometric configurations. The m(k)-accessibility is an universal concept underlying all kinds of 2-dimensional systems with a center. Numerical calculations have been performed to reveal the electronic structures of the states of the dots with 9 and 19 electrons,respectively. This paper supports the Laughlin wave finction and the composite fermion model from the aspect of symmetry.Comment: Two figure

A new flat shell finite element for the linear analysis of thin shell structures

In this paper, a new rectangular flat shell element denoted ‘ACM_RSBE5’ is presented. The new element is obtained by superposition of the new strain-based membrane element ‘RSBE5’ and the well-known plate bending element ‘ACM’. The element can be used for the analysis of any type of thin shell structures, even if the geometry is irregular. Comparison with other types of shell elements is performed using a series of standard test problems. A correlation study with an experimentally tested aluminium shell is also conducted. The new shell element proved to have a fast rate of convergence and to provide accurate results