On the Compatibility Equations in Geometrically Exact Beam Finite Element

2016 ◽  
Author(s):  
Valentin Sonneville ◽  
Olivier A. Bauchau ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Spatial Interpolation ◽  
Dynamic Equilibrium ◽  
Beam Theory ◽  
Body Motion ◽  
Equilibrium Equations ◽  
Path Independence ◽  
Geometrically Exact Beam ◽  
Geometrically Exact Beam Theory

This paper discusses the compatibility equations which relate the velocity field and the strain field in geometrically exact beam theory. The analysis is carried out in the context of intrinsic equations, namely the dynamic equilibrium equations are formulated in terms of local velocities and strains only. In addition to the well established objectivity and path-independence requirements of the spatial discretization, these compatibility equations show that a consistent spatial interpolation of the velocity field should depend on the curvature of the beam, including initial curvature and curvature from the deformation, and it is shown that this consistency is connected to the ability of the finite element to represent exactly rigid body motion velocities. A two node interpolation scheme is studied and it appears that, as the element gets smaller under mesh refinement, the effect of this dependency reduces, leading eventually to the classical linear shape functions.

Efficient Finite Element for Evaluation of Strain Concentrations in Concrete Coated Pipelines

2008 ◽  
Author(s):  
Svein Sævik ◽  
Martin Storheim ◽  
Erik Levold
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Material Model ◽  
Body Motion ◽  
Theoretical Formulation ◽  
Concrete Material ◽  
Non Linear ◽  
Full Scale Tests

MARINTEK has developed software for detailed analysis of pipelines during installation and operation. As part of the software development a new coating finite element was developed in cooperation with StatoilHydro enabling efficient analysis of field joint strain concentrations of long concrete coated pipeline sections. The element was formulated based on sandwich beam theory and application of the Principle of Potential Energy. Large deformations and non-linear geometry effects were handled by a Co-rotated “ghost” reference description where elimination of rigid body motion was taken care of by referring to relative displacements in the strain energy term. The non-linearity related to shear interaction and concrete material behaviour was handled by applying non-linear springs and a purpose made concrete material model. The paper describes the theoretical formulation and numerical studies carried out to verify the model. The numerical study included comparison between model and full-scale tests as well as between model and other commercial software. At last a 3000 m long pipeline was analysed to demonstrate the strain concentration behaviour of a concrete coated pipeline exposed to high temperature snaking on the seabed.

scholarly journals High-Efficiency Dynamic Modeling of a Helical Spring Element Based on the Geometrically Exact Beam Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jian Zhang ◽  
Zhaohui Qi ◽  
Gang Wang ◽  
Shudong Guo
Keyword(s):  
High Efficiency ◽  
Curvature Vector ◽  
Polar Angle ◽  
Beam Theory ◽  
High Frequency Oscillation ◽  
Helical Spring ◽  
Static Stiffness ◽  
Spring Element ◽  
Geometrically Exact Beam ◽  
Geometrically Exact Beam Theory

This paper presents a modeling study of the dynamics of a helical spring element with variable pitch and radius considering both the static stiffness and dynamic response by using the geometrically exact beam theory. The geometrically exact beam theory based on the Euler–Bernoulli beam hypothesis is described, of which the shear deformations are ignored. Unlike the traditional spliced curved beam element method, the helical spring element is described with curvature vector and axial strain by establishing and spline-interpolating a function of the radius, the height, the polar angle, and the torsion angle of the whole spring. In addition, a model smoothing method is developed and applied in the numerical analysis to filter the high-frequency oscillation component of the flexible multibody systems, so as to correct the system dynamic equations and improve the calculation efficiency when solving the static equilibrium of the spring. This study also carries out five numerical trials to validate the above dynamic procedure of the helical spring element. The example of the spring static stiffness design shows that the proposed helical spring procedure enables one to deal with practical engineering applications.

Ultimate strength of steel beam-columns under axial compression

2017 ◽  
Vol 231 (4) ◽  
pp. 828-843
Author(s):  
Zhongwei Li ◽  
Mayuresh Patil ◽  
Xiaochuan Yu
Keyword(s):  
Ultimate Strength ◽  
Axial Compression ◽  
Beam Theory ◽  
Computer Code ◽  
Offshore Structures ◽  
Element Analysis ◽  
Beam Columns ◽  
Geometrically Exact Beam ◽  
Steel Panels ◽  
Geometrically Exact Beam Theory

This article presents a semi-analytical method to calculate the ultimate strength of inelastic beam-columns with I-shaped cross section using geometrically exact beam theory. A computer code based on this method has been applied to beam-columns under axial compression. The results agree with nonlinear finite element analysis. Compared with previous step-by-step integration approach, this new method is more efficient and can be extended to multi-span beam-columns and other load combinations including lateral pressure. The presented beam-column model is ideally suited for ultimate strength prediction of stiffened steel panels of ships and offshore structures.

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