A simplified plane strain analysis of lateral wall deflection for excavations with cross walls

2012 ◽  
Vol 49 (10) ◽  
pp. 1134-1146 ◽  
Author(s):  
Pio-Go Hsieh ◽  
Chang-Yu Ou ◽  
Chiang Shih
Keyword(s):  
Plane Strain ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Lateral Wall ◽  
Diaphragm Wall ◽  
Beam Model ◽  
Two Dimensional ◽  
Wall Deflection ◽  
Dimensional Plane ◽  
Proposed Model

Previous studies have shown that installation of cross walls in deep excavations can reduce lateral wall deflection to a very small amount. To predict the lateral wall deflection for excavations with cross walls, it is necessary to perform a three-dimensional numerical analysis because the deflection behavior of the diaphragm wall with cross walls is by nature three dimensional. However for the analysis and design of excavations, two-dimensional plane strain analysis is mostly used in practice . For this reason, based on the deflection behavior of continuous beams and the superimposition principle, an equivalent beam model suitable for two-dimensional plane strain analysis was derived to predict lateral wall deflection for excavations with cross walls. Three excavation cases were employed to verify the proposed model. Case studies confirm the proposed equivalent beam model for excavations with cross walls installed from near the ground surface down to at least more than half the embedded depth of the diaphragm wall. For the case with a limited cross-wall depth, the proposed model yields a conservative predicted lateral wall deflection.

Two-Dimensional Green’s Functions for Elastic Bi-materials

1992 ◽  
Vol 59 (2) ◽  
pp. 321-327 ◽  
Author(s):  
J. L. Carvalho ◽  
J. H. Curran
Keyword(s):  
Boundary Element Method ◽  
Hydraulic Fracturing ◽  
Boundary Element ◽  
Plane Strain ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Dimensional Plane ◽  
Element Method

Two-dimensional plane-strain fundamental solutions for elastic bi-materials are developed using the nuclei of strain method. The method is a reduction of the threedimensional approach previously derived by Vijayakumar and Cormack. The structure of the three-dimensional solution is preserved and the two-dimensional nuclei of strain and their corresponding vector functions are reported in this paper. Application of these solutions to the boundary element method is demonstrated via a hydraulic fracturing example.

Three-dimensional analysis of soil – steel bridges

1995 ◽  
Vol 22 (6) ◽  
pp. 1155-1163 ◽  
Author(s):  
Youssef Girges ◽  
George Abdel-Sayed
Keyword(s):  
Plane Strain ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Middle Part ◽  
Steel Bridges ◽  
Steel Shell ◽  
Live Load ◽  
Two Dimensional ◽  
Element Analysis

The present design of soil–steel bridges is based on plane-strain analysis by considering a slice of a unit width of the conduit wall and the surrounding soil. This two-dimensional analysis neglects the third-dimensional effect of the steel shell and the soil continuum which could be significant especially when the load varies in the longitudinal direction, as in the case of live load acting over a shallow cover. The structure is also subjected to a varying dead load due to the variation in the depth of cover from maximum at the middle part of the conduit to zero at the conduit edges. A three-dimensional finite element analysis is presented in this paper to examine the actual three-dimensional behaviour of soil-steel bridges. The thrust and bending moment around the conduit walls as well as the stability of a single conduit are presented and compared with the results obtained from plane-strain analysis. Also, the live load dispersion in the soil above the conduit is examined and compared with some present codes. The study leads to evaluation of the degree of approximation inherited with the practical approaches of the two-dimensional analysis. Key words: conduit, corrugated steel, three-dimensional analysis, stability, soil–steel bridges.

Inclusion of Local Shell Behavior of Tubes Into a Two-Dimensional Beam Approximation of Deformation in Nuclear Fuel Channels

2002 ◽  
Author(s):  
S. Khajehpour ◽  
R. G. Sauve´ ◽  
N. Badie
Keyword(s):  
Finite Element ◽  
Contact Stiffness ◽  
Three Dimensional ◽  
Local Deformation ◽  
Beam Model ◽  
Two Dimensional ◽  
Dimensional Modeling ◽  
Dimensional Finite Element ◽  
Nonlinear Force ◽  
Three Dimensional Finite Element

A method has been developed to incorporate the local three-dimensional shell behavior of two concentric tubes in the two-dimensional beam modeling of the problem. The two dimensional modeling of fuel channels in CANDU pressurized heavy water nuclear reactors is used in lieu of a more accurate three dimensional finite element approach in order to reduce the on-line simulation time which greatly affects the SLAR (Spacer Location And Repositioning) maintenance operation cost during outage. However, effort must be made to include the three-dimensional shell behavior of these channels into the two-dimensional modeling. In recent studies a nonlinear force-dependent model for contact stiffness between the calandria tube and pressure tube has been developed. However, local deformation of calandria the tube at spacer locations due to in-reactor creep leads to settling of the spacer into the calandria tube that consequently reduces the gap between the two tubes. In this work, the effect of local deformation (elastic and creep) of calandria tubes on modeling of contact at spacer locations is assessed using a three dimensional finite element code. The result is incorporated into a two-dimensional beam model of the problem as a reduction in size of the spacers that separate the two tubes. It is shown that the proposed method increases the accuracy of prediction of contact time and the spacer. In general, the method described in this paper suggests a way to incorporate local shell deformation into beam models of slender shell structure.

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.

Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

2022 ◽  
pp. 108128652110679
Author(s):  
Emilio Turco
Keyword(s):  
Kinetic Energy ◽  
Strain Energy ◽  
Nonlinear Vibrations ◽  
Three Dimensional ◽  
Integration Scheme ◽  
Beam Model ◽  
Model Formulation ◽  
Discrete Approach ◽  
Numerical Integration Scheme ◽  
Proposed Model

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

Stereographic Visual Displays and the Three-Dimensional Communication of Findings in Marketing Research

1997 ◽  
Vol 34 (4) ◽  
pp. 526-536 ◽  
Author(s):  
Morris B. Holbrook
Keyword(s):  
Three Dimensional ◽  
Marketing Research ◽  
Two Dimensional ◽  
Visual Displays ◽  
Structural Patterns ◽  
Dimensional Plane ◽  
Present Complex ◽  
Key Concepts

In their attempts to communicate with managers and other interested readers, marketing researchers frequently present complex findings in various sorts of visual displays. These diagrams, charts, maps, pictures, and other figures help elucidate the nature of the relationships and structural patterns involved. However, their ability to communicate is partially limited by their typical restriction to the two-dimensional plane of the printed page. As an aid to overcoming such problems, stereographic techniques permit the construction of three-dimensional representations whose vividness and depth provide greater clarity and enhance interpretability to strengthen the reader's grasp of key concepts. The author illustrates the stereographic approach to three-dimensional communication using general examples closely analogous to relevant applications in marketing research.

Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites

2011 ◽  
Vol 137 ◽  
pp. 1-6
Author(s):  
Qing Li ◽  
Xiao Xiang Yang
Keyword(s):  
Carbon Black ◽  
Mechanical Behavior ◽  
Plane Stress ◽  
Volume Fraction ◽  
Filler Particle ◽  
Three Dimensional ◽  
Rubber Matrix ◽  
Two Dimensional ◽  
Rubber Composites ◽  
Dimensional Plane

In this paper, the micromechanical finite element method based on Representative Volume Element has been applied to study and analyze the macro mechanical properties of the carbon black filled rubber composites by using two-dimensional plane stress simulations and three-dimensional axisymmetric simulations under uniaxial compression respectively. The dependence of the macroscopic stress-strain behavior and the effective elastic modulus of the composites, on particle shape, particle area/volume fraction and particle stiffness has been investigated and discussed. Additionally, the simulation results of the two-dimensional plane stress model and the three-dimensional axisymmetric model are evaluated and compared with the experimental data, which shows that the two-dimensional plane stress simulations generate poor predictions on the mechanical behavior of the carbon black particle reinforced rubber composites, while the three-dimensional axisymmetric simulations appear to give a better prediction.

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