scholarly journals Guaranteed Lower Bounds for the Elastic Eigenvalues by Using the Nonconforming Crouzeix–Raviart Finite Element

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1252
Author(s):  
Xuqing Zhang ◽  
Yu Zhang ◽  
Yidu Yang
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Lower Bounds ◽  
Numerical Experiments ◽  
Displacement Boundary Condition ◽  
Eigenvalue Bounds ◽  
Displacement Boundary ◽  
Linear Elastic ◽  
Matlab Program

This paper uses a locking-free nonconforming Crouzeix–Raviart finite element to solve the planar linear elastic eigenvalue problem with homogeneous pure displacement boundary condition. Making full use of the Poincaré inequality, we obtain the guaranteed lower bounds for eigenvalues. Besides, we also use the nonconforming Crouzeix–Raviart finite element to the planar linear elastic eigenvalue problem with the pure traction boundary condition, and obtain the guaranteed lower eigenvalue bounds. Finally, numerical experiments with MATLAB program are reported.

scholarly journals Material property and boundary condition effects on stresses in avalanche snow-packs

1974 ◽  
Vol 13 (67) ◽  
pp. 99-108 ◽  
Author(s):  
J. O. Curtis ◽  
F. W. Smith
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Stress Distribution ◽  
Computer Program ◽  
Material Properties ◽  
Shear Failure ◽  
Stress Distributions ◽  
Snow Pack ◽  
Snow Layer ◽  
Linear Elastic

A linear elastic finite element computer program was applied to determine the stress distributions in multi-layered snow-packs typical of those found at Berthoud Pass, Colorado. The effect on stress distribution of wide variations in elastic material properties was examined. Also, an attempt was made to model the shear failure of a weak sub-layer in the snow-pack by relaxing the condition that the bottom snow layer be firmly attached to the ground.

scholarly journals Material property and boundary condition effects on stresses in avalanche snow-packs

1974 ◽  
Vol 13 (67) ◽  
pp. 99-108 ◽  
Author(s):  
J. O. Curtis ◽  
F. W. Smith
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Stress Distribution ◽  
Computer Program ◽  
Material Properties ◽  
Shear Failure ◽  
Stress Distributions ◽  
Snow Pack ◽  
Snow Layer ◽  
Linear Elastic

A linear elastic finite element computer program was applied to determine the stress distributions in multi-layered snow-packs typical of those found at Berthoud Pass, Colorado. The effect on stress distribution of wide variations in elastic material properties was examined. Also, an attempt was made to model the shear failure of a weak sub-layer in the snow-pack by relaxing the condition that the bottom snow layer be firmly attached to the ground.

Similarity Solution for the Synchronous Grouting of Shield Tunnel Under the Vertical Non-Axisymmetric Displacement Boundary Condition

2016 ◽  
Vol 9 (1) ◽  
pp. 205-232 ◽  
Author(s):  
Jinfeng Zou ◽  
Songqing Zuo
Keyword(s):  
Boundary Condition ◽  
Similarity Solution ◽  
Ground Surface ◽  
Vertical Displacement ◽  
Vertical Surface ◽  
Parameter Analysis ◽  
Shield Tunnel ◽  
Displacement Boundary Condition ◽  
Displacement Boundary ◽  
Grouting Pressure

AbstractSimilarity solution is investigated for the synchronous grouting of shield tunnel under the vertical non-axisymmetric displacement boundary condition in the paper. The synchronous grouting process of shield tunnel was simplified as the cylindrical expansion problem, which was based on the mechanism between the slurry and stratum of the synchronous grouting. The stress harmonic function on the horizontal and vertical ground surfaces is improved. Based on the virtual image technique, stress function solutions and Boussinesq's solution, elastic solution under the vertical non-axisymmetric displacement boundary condition on the vertical surface was proposed for synchronous grouting problems of shield tunnel. In addition, the maximum grouting pressure was also obtained to control the vertical displacement of horizontal ground surface. The validity of the proposed approach was proved by the numerical method. It can be known from the parameter analysis that larger vertical displacement of the horizontal ground surface was induced by smaller tunnel depth, smaller tunnel excavation radius, shorter limb distance, larger expansion pressure and smaller elastic modulus of soils.

Modeling Input Motion Boundary Conditions for Simulations of Geotechnical Shaking Table Tests

2010 ◽  
Vol 26 (2) ◽  
pp. 349-369 ◽  
Author(s):  
Mahadevan Ilankatharan ◽  
Bruce Kutter
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Shaking Table ◽  
Experimental Result ◽  
Displacement Boundary Condition ◽  
Displacement Boundary ◽  
Input Motion ◽  
Displacement Approach ◽  
Table Motion ◽  
Motion Boundary

This paper discusses the effects of using different input-motion-boundary-conditions on the sensitivity of numerical simulations results to errors in material properties of a specimen tested on a shaking table. In the flexible-actuator-prescribed-force-boundary-condition, input is specified by a force across an actuator element that connects the shaking table to a reaction mass. In the prescribed-displacement-boundary-condition, the measured shaking table motion in the experiment is prescribed in the simulation. The flexible-actuator-prescribed-force approach yielded smaller, almost constant sensitivity of simulation results to input properties. The prescribed-displacement approach yielded larger and more variable sensitivities. The sensitivity of results depends on the how the boundary conditions are handled has further implications: the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions on the comparison, and numerically determined sensitivities may not be physically meaningful if the boundary condition is not accurately modeled.

scholarly journals Study on the Generalized Displacement Boundary and Its Analytical Prediction for Ground Movements Induced by Shield Tunneling

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Qianlong Tang ◽  
Fudong Chen ◽  
Mingfeng Lei ◽  
Binbin Zhu ◽  
Limin Peng
Keyword(s):  
Boundary Condition ◽  
Ground Movement ◽  
Shield Tunnel ◽  
Analytical Prediction ◽  
Displacement Boundary Condition ◽  
Shield Tunneling ◽  
Displacement Boundary ◽  
Ground Movements ◽  
Gap Parameter ◽  
Tunnel Depth

The process of shield tunnel excavation would inevitably cause surrounding ground movement, and excessive displacement in the soil could lead to large deformation and even collapse of the tunnel. The methods estimating convergence deformation around tunnel opening is summarized. Then, a universal pattern of displacement boundary condition around the tunnel cavity is originally introduced, which is solved as the combination of three fundamental deformation modes, namely, uniform convergence, vertical translation, and ovalization. The expression for the above-mentioned displacement boundary condition is derived, by imposing which the analytical solution for ground movements, based on the stress function method, is proposed. The reliability and applicability of this proposed solution are verified by comparing the observed data in terms of surface settlement, underground settlement, and horizontal displacement. Further parametric analyses indicate the following: (1) the maximum settlement increases linearly with the gap parameter and the tunnel radius, while it is negatively related to the tunnel depth; (2) the trough width parameter is independent of the gap parameter and the radius, while it is proportional to the tunnel depth. This study provides a new simple and reliable method for predicting ground movements induced by shield tunneling.

scholarly journals Estimation Modal Parameter Variation with Respect to Internal Energy Variation Based on the Iwan Model

2019 ◽  
Vol 9 (20) ◽  
pp. 4290 ◽  
Author(s):  
Jongsuh Lee
Keyword(s):  
Boundary Condition ◽  
Internal Energy ◽  
Estimation Method ◽  
Harmonic Excitation ◽  
Mode Analysis ◽  
Displacement Boundary Condition ◽  
Displacement Boundary ◽  
Double Beam ◽  
Full Structure ◽  
Two Parameters

Typical factors that cause nonlinear behavior in structures are geometric nonlinearity, force and displacement boundary condition nonlinearities, and material nonlinearity. The nonlinearity caused by an increase of the internal energy in built-up structures is mostly due to the displacement boundary condition induced by the contact interface region. This study proposes an experimental mode analysis technique that predicts changes in natural frequencies and damping ratios when the external excitation force increases in a structure’s contact surfaces. Specifically, the nonlinearity of the dynamic characteristics induced by the contact region is described by the constitutive Iwan model. Next, an estimation method was developed for two parameters among the four of the Iwan model. This study used a modal analysis method. As an extension of a previous study, the approximate form of the harmonic excitation-induced force was determined in closed form. The configuration of the numerical model for the full structure was introduced from this resultant form. By using these numerical results, responses in the full structure, according to the harmonic excitation, have been represented in mode summation form. This research proposes an estimation method for two parameters among the four of the constitutive model. The proposed method was verified by simulations conducted with the lumped model and by experiments conducted on a partially connected double beam.

Constrained displacement boundary condition in embedment testing of dowel-type fasteners in LVL

Strain ◽  
2017 ◽  
Vol 53 (6) ◽  
pp. e12238 ◽  
Author(s):  
Michael Schweigler ◽  
Thomas K. Bader ◽  
Johan Vessby ◽  
Josef Eberhardsteiner
Keyword(s):  
Boundary Condition ◽  
Displacement Boundary Condition ◽  
Displacement Boundary

scholarly journals What Can Go Wrong

1998 ◽  
Vol 120 (05) ◽  
pp. 63-65 ◽  
Author(s):  
Klaus-Jürgen Bathe
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Computation Time ◽  
Displacement Boundary ◽  
Linear Elastic ◽  
Stiffness Matrices ◽  
Great Confidence ◽  
Support Conditions ◽  
Material Conditions ◽  
Displacement Based

This article focuses on some aspects of the reliability of finite-element methods and their accurate use. In order to illustrate, linear elastic solutions are considered and assumed that the algebraic finite-element equations are solved exactly. The mathematical model is based on assumptions made regarding the geometry, material conditions, loading, and displacement boundary conditions. The analysis problem is obtained by specifying the geometry and dimensions, support conditions, material constants, and loading. As a remedy in displacement-based finite-element methods, reduced integration is employed. This means that in the numerical integration of the element stiffness matrices, the exact matrices are not evaluated. The method is simple to program and requires less computation time to establish the matrices, and with experience acceptable results are frequently obtained. However, the technique can also lead to very large errors. As a conclusion, finite-element methods can now be employed with great confidence, however, only the methods considered reliable should be used.

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