Numerical Solutions to Single-Curvature Bending Problems

2000 ◽  
Vol 6 (5) ◽  
pp. 351-356
Author(s):  
Edvard Michnevič ◽  
Rimantas Belevičius

The new finite element of multilayered built up with an arbitrary series of layers plate for plate bending problem is formulated on the ground of widely used, effective finite element Discrete Kirchhof Theory (DKT). The material of each layer is supposed to be different and orthotopic. Triangular element has 6 d.o.f.'s at each of 3 nodal points: 3 displacements and 2 rotations about co-ordinate axes. The 6th fictitious rotation about axis perpendicular to the element is also introduced due to numerical requirements. The element takes into account all the in-plane/out-of-plane effects except the shear. The element could find an application in the slab bending problems or in the plate, where the shear influence could be neglected, bending problems. The numerical examples are presented. Present solutions are compared with available analytical and numerical solutions.


2007 ◽  
Vol 13 (1) ◽  
pp. 41-46
Author(s):  
Edvard Michnevič

The new finite element of multilayered built up with an arbitrary series of layers plate for plate bending problem is formulated on the ground of widely used, effective finite element Discrete Kirchhof Theory (DKT). The material of each layer is supposed to be different and orthotropic. Triangular element has 6 d.o.f.’s at each of 3 nodal points: 3 displacements and 3 rotations about co‐ordinate axes. The element takes into account all the in‐plane/out‐of‐plane effects except for shear. The element could find an application in the slab bending problems or in the plate, where the shear influence could be neglected, bending problems. Numerical examples are presented. Present solutions are compared with available analytical and numerical solutions.


Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Abdallah Zatar ◽  
Djamal Hamadi

The purpose of this paper is to present the formulation of a new sector finite element based on the strain approach for the numerical analysis of circular thin plate bending. The element is named SBSPK and has four nodes and three degrees of freedom per node (3 d.o.f./node). From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The results obtained are compared with analytical and available numerical solutions.


Author(s):  
Huynh Huu Tai ◽  
Nguyen Van Hieu ◽  
Vu Duy Thang

In this paper the smoothed four-node element with in-plane rotations MISQ24 is combined with a C0-type higher-order shear deformation theory (C0-HSDT) to propose an improved linear quadrilateral plate element for static and free vibration analyses of laminated composite plates. This improvement results in two additional degrees of freedom at each node and require no shear correction factors while ensuring the high precision of numerical solutions. Composite plates with different lay-ups, boundary conditions and various geometries such as rectangular, skew and triangular plates are analyzed using the proposed element. The obtained numerical results are compared with those from previous studies in the literature to demonstrate the effectiveness, the reliability and the accuracy of the present element. Keywords: composite laminated plates; bending problems; free vibration; C0-HSDT; MISQ24.


Author(s):  
D.E. Jesson ◽  
S. J. Pennycook

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;


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