Structural Analysis of Arches in Plane with a Family of Simple and Accurate Curved Beam Elements Based on Mindlin-Reissner Model

2011 ◽  
Vol 27 (1) ◽  
pp. 129-138 ◽  
Author(s):  
N. Tayşi ◽  
M. T. Göĝüş ◽  
M. Özakça
Keyword(s):  
Finite Element ◽  
Structural Analysis ◽  
Numerical Methods ◽  
Variable Thickness ◽  
Element Formulation ◽  
Curved Beam ◽  
Rotatory Inertia ◽  
Inertia Effects ◽  
Beam Elements ◽  
Arch Structures

ABSTRACTIn this paper, the basic finite element formulation of a newly developed family of variable thickness, curved,C(0) continuity Mindlin-Reissner model curved beam elements which include shear deformation and rotatory inertia effects is presented. The accuracy, convergence and efficiency of these newly developed curved beam elements are explored through a series of analyses of arch structures and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements.

scholarly journals Corotational Finite Element Formulation for Static Nonlinear Analyses with Enriched Beam Elements

AIAA Journal ◽  
2020 ◽  
Vol 58 (5) ◽  
pp. 2276-2292
Author(s):  
T. Macquart ◽  
S. Scott ◽  
P. Greaves ◽  
P. M. Weaver ◽  
A. Pirrera
Keyword(s):  
Finite Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Nonlinear Analyses ◽  
Beam Elements

A Finite Element Modeling Framework for Planar Curved Beam Dynamics Considering Nonlinearities and Contacts

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Tianheng Feng ◽  
Soovadeep Bakshi ◽  
Qifan Gu ◽  
Dongmei Chen
Keyword(s):  
Finite Element ◽  
Beam Dynamics ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Modeling Framework ◽  
External Wall ◽  
Beam Elements ◽  
High Compression ◽  
Assumed Strain

Motivated by modeling directional drilling dynamics where planar curved beams undergo small displacements, withstand high compression forces, and are in contact with an external wall, this paper presents an finite element method (FEM) modeling framework to describe planar curved beam dynamics under loading. The shape functions of the planar curved beam are obtained using the assumed strain field method. Based on the shape functions, the stiffness and mass matrices of a planar curved beam element are derived using the Euler–Lagrange equations, and the nonlinearities of the beam strain are modeled through a geometric stiffness matrix. The contact effects between curved beams and the external wall are also modeled, and corresponding numerical methods are discussed. Simulations are carried out using the developed element to analyze the dynamics and statics of planar curved structures under small displacements. The numerical simulation converges to the analytical solution as the number of elements increases. Modeling using curved beam elements achieves higher accuracy in both static and dynamic analyses compared to the approximation made by using straight beam elements. To show the utility of the developed FEM framework, the post-buckling condition of a directional drill string is analyzed. The drill pipe undergoes spiral buckling under high compression forces, which agrees with experiments and field observations.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

Weak Form Quadrature Element Analysis of Diaphragm Walls

2014 ◽  
Vol 580-583 ◽  
pp. 380-385
Author(s):  
Ye Li ◽  
Hong Zhi Zhong
Keyword(s):  
Finite Element ◽  
Earth Pressure ◽  
Weak Form ◽  
Element Formulation ◽  
Element Analysis ◽  
Complex Load ◽  
Beam Elements ◽  
Finite Element Software ◽  
Load Distributions ◽  
Diaphragm Walls

In combination with Rankine's earth pressure theory, a weak form quadrature element formulation is established for analysis of diaphragm walls. Results are compared with those of Paroi2, a finite element software package for diaphragm walls, to demonstrate the effectiveness and the advantages of the present formulation. Accurate results are obtained with only a few weak form quadrature beam elements, contrasting with dense finite element division that is needed for complex load distributions over the diaphragm wall.

scholarly journals Evaluating the Seismic Capacity of Dry-Joint Masonry Arch Structures via the Combined Finite-Discrete Element Method

2021 ◽  
Vol 11 (18) ◽  
pp. 8725
Author(s):  
Wangpeng Li ◽  
Xudong Chen ◽  
Hongfan Wang ◽  
Andrew H. C. Chan ◽  
Yingyao Cheng
Keyword(s):  
Finite Element ◽  
Discrete Element Method ◽  
Discrete Element ◽  
Element Formulation ◽  
Discrete Elements ◽  
Seismic Capacity ◽  
Masonry Arch ◽  
Highly Nonlinear ◽  
Arch Structures ◽  
Element Method

The behaviour of dry-joint masonry arch structures is highly nonlinear and discontinuous since they are composed of individual discrete blocks. These structures are vulnerable to seismic excitations. It is difficult for traditional methods like the standard finite element method (FEM) to simulate masonry failure due to their intrinsic limitations. An advanced computational approach, i.e., the combined finite-discrete element method (FDEM), was employed in this study to examine the first-order seismic capacity of masonry arches and buttressed arches with different shapes subjected to gravity and constant horizontal acceleration. Within the framework of the FDEM, masonry blocks are discretised into discrete elements. A finite element formulation is implemented into each discrete element, providing accurate predictions of the deformation of each block and contact interactions between blocks. Numerical examples are presented and validated with results from the existing literature, demonstrating that the FDEM is capable of capturing the seismic capacities and hinge locations of masonry arch structures. Further simulations on geometric parameters and friction coefficient of masonry buttressed arches were conducted, and their influences on the seismic capacities are revealed.

scholarly journals Finite-element modelling of elastic wave propagation and scattering within heterogeneous media

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160738 ◽  
Author(s):  
A. Van Pamel ◽  
G. Sha ◽  
S. I. Rokhlin ◽  
M. J. S. Lowe
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Elastic Waves ◽  
Heterogeneous Media ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Polycrystalline Materials ◽  
Element Formulation ◽  
Quantitative Validation

The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.

Sign in / Sign up

Export Citation Format

Share Document