Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

Some modifications for ES-FEM and its application for vehicle design

2015 ◽  
Vol 32 (5) ◽  
pp. 1432-1459 ◽  
Author(s):  
Guanxin Huang ◽  
Hu Wang ◽  
Guangyao Li
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Large Scale ◽  
Local Coordinate System ◽  
Global Coordinate System ◽  
Content Type ◽  
Large Scale Problems ◽  
Edge Based ◽  
Global Stiffness Matrix ◽  
Made In

Purpose – The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study. Design/methodology/approach – First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully. Findings – First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system. Originality/value – The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.

A Central Point-Based Discrete Shear Gap Method for Plates and Shells Analysis Using Triangular Elements

2017 ◽  
Vol 09 (04) ◽  
pp. 1750055 ◽  
Author(s):  
X. Y. Cui ◽  
L. Tian
Keyword(s):  
Local Coordinate System ◽  
Nonlinear Problems ◽  
Shell Element ◽  
Base Point ◽  
Central Point ◽  
Triangular Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Plates And Shells ◽  
Discrete Shear Gap

In this paper, discrete shear gap method (DSG)-based central point of the three-node triangular element (CP-DSG3) is presented for both linear and geometrically nonlinear analysis of plates and shells. A fictitious central point is introduced as the base point of the DSG to overcome the anisotropy of the formerly proposed formulation. In the CP-DSG3, the discrete shear gap at each field node is deduced using rotations of all three nodes in local coordinate system, which makes it an isotropic triangular plate and shell element. At the same time, the CP-DSG3 inherits the advantages of shear-locking-free from the DSG. Moreover, a series of numerical examples consisting of standard patch test, linear and geometrically nonlinear problems have been investigated and the results demonstrate the excellent performance and accuracy of the proposed CP-DSG3.

Study on Establishment and Transformation of Coordinate System of Steel Structure in 3D Software

2014 ◽  
Vol 501-504 ◽  
pp. 2541-2545
Author(s):  
Kai Sun ◽  
Lu Shuang Wei ◽  
Li Xuan ◽  
Lun Gang Zhou
Keyword(s):  
Coordinate System ◽  
3D Visualization ◽  
Local Coordinate System ◽  
Steel Structure ◽  
Structure Design ◽  
Global Coordinate System ◽  
3D Space ◽  
Steel Members ◽  
Safe Condition ◽  
3D Software

The 3D visualization design of steel structure under the CAD environment needs to work in the global coordinate system (WCS), but design of various steel members in the 3D space must be completed in the local coordinate system (UCS), so it is perplexing for the conversion and calculation between UCSi (i=1,2,3....n) and WCS. It is proved that the maize grains are not polluted and food production is in safe condition. The article describes classification of several common coordinate systems, discuss the method of setting up coordinates system. Describe the process of type convertion of coordinate system in steel structure design and detailing softwares, and explained the advantage of the application in the real world project.

A Finite Element Formulation of Flexible Slider Crank Mechanism Using Local Coordinates

1994 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
High Speed ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Local Coordinate System ◽  
Body Motion ◽  
Elastic Displacement ◽  
Global Coordinate System ◽  
Element Formulation

Abstract The need for higher productivity has lead to the design of machines operating at higher speeds. At high speed the rigid body assumption is no longer valid and the links should be considered flexible. In this work a method which is based on Modified Lagrange Equation for modeling flexible mechanism is presented. The method posses a more computational efficiency for not requiring the transformation from the local coordinate system to the global coordinate system. Also an approach using the homogeneous coordinate for element matrices generation is presented. The approach leads to a formalism where the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulations.

A Finite Element Formulation of a Flexible Slider Crank Mechanism Using Local Coordinates

1995 ◽  
Vol 117 (3) ◽  
pp. 329-335 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Local Coordinate System ◽  
Body Motion ◽  
Elastic Displacement ◽  
Global Coordinate System ◽  
Element Formulation ◽  
Crank Mechanism

The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads to a formalism in which the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of the elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulators.

scholarly journals GPS-Free Localization Algorithm for Wireless Sensor Networks

Sensors ◽  
2010 ◽  
Vol 10 (6) ◽  
pp. 5899-5926 ◽  
Author(s):  
Lei Wang ◽  
Qingzheng Xu
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Coordinate System ◽  
Probability Model ◽  
Local Coordinate System ◽  
Convergence Time ◽  
Wireless Sensor ◽  
Global Coordinate System ◽  
Multiplication Factor ◽  
Localization Scheme

Localization is one of the most fundamental problems in wireless sensor networks, since the locations of the sensor nodes are critical to both network operations and most application level tasks. A GPS-free localization scheme for wireless sensor networks is presented in this paper. First, we develop a standardized clustering-based approach for the local coordinate system formation wherein a multiplication factor is introduced to regulate the number of master and slave nodes and the degree of connectivity among master nodes. Second, using homogeneous coordinates, we derive a transformation matrix between two Cartesian coordinate systems to efficiently merge them into a global coordinate system and effectively overcome the flip ambiguity problem. The algorithm operates asynchronously without a centralized controller; and does not require that the location of the sensors be known a priori. A set of parameter-setting guidelines for the proposed algorithm is derived based on a probability model and the energy requirements are also investigated. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results. We also compare the performance of the proposed algorithm under a variety multiplication factor, node density and node communication radius scenario. Experiments show that our algorithm outperforms existing mechanisms in terms of accuracy and convergence time.

Modelling time-dependent mechanical behaviour of softwood using deformation kinetics

Holzforschung ◽  
2011 ◽  
Vol 65 (2) ◽  
Author(s):  
Emil Tang Engelund ◽  
Staffan Svensson
Keyword(s):  
Coordinate System ◽  
Mechanical Behaviour ◽  
Local Coordinate System ◽  
Microfibril Angle ◽  
Significant Degree ◽  
Local System ◽  
Time Dependent ◽  
Global Coordinate System ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

Abstract The time-dependent mechanical behaviour (TDMB) of softwood is relevant, e.g., when wood is used as building material where the mechanical properties must be predicted for decades ahead. The established mathematical models should be able to predict the time-dependent behaviour. However, these models are not always based on the actual physical processes causing time-dependent behaviour and the physical interpretation of their input parameters is difficult. The present study describes the TDMB of a softwood tissue and its individual tracheids. A model is constructed with a local coordinate system that follows the microfibril orientation in the S2 layer of the cell wall. The inclination of the local system to the global coordinate system reflects the microfibril angle of the tracheid. Normal excitations in the local system perform linear elastically, whereas shearing excitation in the local system produces both elastic and inelastic responses. The results of the model are compared with experimental results of different types. It was observed that the model is able to describe the results. Moreover, to some surprise, the introduction of only elastic and viscous properties on the microscopic scale leads to an apparent macroscopic viscoelasticity, i.e., the time-dependent processes are to a significant degree reversible.

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