Coupling three‐dimensional peridynamics and high‐order one‐dimensional finite elements based on local elasticity for the linear static analysis of solid beams and thin‐walled reinforced structures

2020 ◽  
Vol 121 (22) ◽  
pp. 5066-5081 ◽  
Author(s):  
A. Pagani ◽  
E. Carrera
Keyword(s):  
Finite Elements ◽  
Static Analysis ◽  
Three Dimensional ◽  
High Order ◽  
One Dimensional ◽  
Thin Walled ◽  
Linear Static Analysis

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

scholarly journals Established Numerical Techniques for the Structural Analysis of a Regional Aircraft Landing Gear

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
F. Caputo ◽  
A. De Luca ◽  
A. Greco ◽  
A. Marro ◽  
A. Apicella ◽  
...  
Keyword(s):  
Finite Elements ◽  
Numerical Models ◽  
Three Dimensional ◽  
Landing Gear ◽  
Point Of View ◽  
Fe Model ◽  
One Dimensional ◽  
Reaction Forces ◽  
Local Technique ◽  
Stick Model

Usually during the design of landing gear, simplified Finite Element (FE) models, based on one-dimensional finite elements (stick model), are used to investigate the in-service reaction forces involving each subcomponent. After that, the design of such subcomponent is carried out through detailed Global/Local FE analyses where, once at time, each component, modelled with three-dimensional finite elements, is assembled into a one-dimensional finite elements based FE model, representing the whole landing gear under the investigated loading conditions. Moreover, the landing gears are usually investigated also under a kinematic point of view, through the multibody (MB) methods, which allow achieving the reaction forces involving each subcomponent in a very short time. However, simplified stick (FE) and MB models introduce several approximations, providing results far from the real behaviour of the landing gear. Therefore, the first goal of this paper consists of assessing the effectiveness of such approaches against a 3D full-FE model. Three numerical models of the main landing gear of a regional airliner have been developed, according to MB, “stick,” and 3D full-FE methods, respectively. The former has been developed by means of ADAMS® software, the other two by means of NASTRAN® software. Once this assessment phase has been carried out, also the Global/Local technique has verified with regard to the results achieved by the 3D full-FE model. Finally, the dynamic behaviour of the landing gear has been investigated both numerically and experimentally. In particular, Magnaghi Aeronautica S.p.A. Company performed the experimental test, consisting of a drop test according to EASA CS 25 regulations. Concerning the 3D full-FE investigation, the analysis has been simulated by means of Ls-Dyna® software. A good level of accuracy has been achieved by all the developed numerical methods.

Modeling of a Beam and a Rotor with an Edge Crack Using Dissimilar Elements

2003 ◽  
Vol 9 (10) ◽  
pp. 1159-1187 ◽  
Author(s):  
A. Nandi ◽  
S. Neogy
Keyword(s):  
Finite Elements ◽  
Stress Field ◽  
Edge Crack ◽  
Three Dimensional ◽  
Transition Element ◽  
Two Dimensional ◽  
Cracked Beam ◽  
One Dimensional ◽  
Beam Elements ◽  
Dimensional Plane

Vibration-based diagnostic methods are used for the detection of the presence of cracks in beams and other structures. To simulate such a beam with an edge crack, it is necessary to model the beam using finite elements. Cracked beam finite elements, being one-dimensional, cannot model the stress field near the crack tip, which is not one-dimensional. The change in neutral axis is also not modeled properly by cracked beam elements. Modeling of such beams using two-dimensional plane elements is a better approximation. The best alternative would be to use three-dimensional solid finite elements. At a sufficient distance away from the crack, the stress field again becomes more or less one-dimensional. Therefore, two-dimensional plane elements or three-dimensional solid elements can be used near the crack and one-dimensional beam elements can be used away from the crack. This considerably reduces the required computational effort. In the present work, such a coupling of dissimilar elements is proposed and the required transition element is formulated. A guideline is proposed for selecting the proper dimensions of the transition element so that accurate results are obtained. Elastic deformation, natural frequency and dynamic response of beams are computed using dissimilar elements. The finite element analysis of cracked rotating shafts is complicated because of the fact that elastic deformations are superposed on the rigid-body motion (rotation about an axis). A combination of three-dimensional solid elements and beam elements in a rotating reference is proposed here to model such rotors.

The method of finite spheres in three-dimensional linear static analysis

2016 ◽  
Vol 173 ◽  
pp. 161-173 ◽  
Author(s):  
Benjamin Lai ◽  
Klaus-Jürgen Bathe
Keyword(s):  
Static Analysis ◽  
Three Dimensional ◽  
Finite Spheres ◽  
Linear Static Analysis

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

High order thin-walled solid finite elements applied to elastic spring-back computations

2006 ◽  
Vol 195 (41-43) ◽  
pp. 5377-5389 ◽  
Author(s):  
Alexander Muthler ◽  
Alexander Düster ◽  
Wolfram Volk ◽  
Marcus Wagner ◽  
Ernst Rank
Keyword(s):  
Finite Elements ◽  
High Order ◽  
Spring Back ◽  
Thin Walled ◽  
Solid Finite Elements ◽  
Elastic Spring
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