Beam unit counting method with thickness

A calculation method and finite element technology, applied in the direction of architecture, building structure, etc., can solve the problems of inconvenience, programming processing difficulties, large calculation errors of deformed units, etc.

Inactive Publication Date: 2007-02-14
TONGJI UNIV
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Problems solved by technology

However, since the secondary lining of the tunnel is mainly a bending component, it is known from the knowledge of material mechanics that the order of the perturbation function of the lining structure is generally relatively high, so it is necessary to distribute several layers of low-order elements along the thickness direction (generally 5 layers). Or use a layer of high-order elements to analyze to achieve sufficient accuracy, which brings certain difficulties to programming and actual calculation: the thickness of the lining is generally relatively thin, and a few layers of low-order elements along the thickness direction will require a lot of discrete elements , and may cause large calculation errors due to deformed elements; while high-order elements using finite elements will have nodes in the edges, and sometimes for the convenience of stratum and structure discretization and the need to control the total solution degrees of freedom, etc., It requires the use of transition units, which brings difficulties to pre-processing and programming. Of course, the difficulties are relative. With the development of computer graphics technology and pre-processing technology, high-order isoparametric units and transition units are often used to a certain extent.
[0004] Low-order elements are widely used in numerical calculations of geotechnical engineering because of their convenient pre-processing grid discretization. more inconvenience

Method used

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  • Beam unit counting method with thickness
  • Beam unit counting method with thickness

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0073] Embodiment 1: cantilever beam

[0074] like Figure 5 The shown cantilever beam is subjected to a vertically downward uniform force p=5kN / m at the end, thickness t=1m, length l=10m, and width h=1m. The elastic modulus of the material E=2.8×10 7 kPa, Poisson's ratio μ = 0.2, excluding self-weight.

[0075] Table 1 Comparison of bending moment (kN.m) between the beam element method and the generalized beam element method

[0076]

[0077] The calculation result with beam element is as follows Image 6 shown. The results of beam bending distance calculated by generalized beam element are as follows: Figure 7 Shown, compared with the beam element calculation results are listed in Table 1. The bending moment of the beam element obtained by using the generalized beam element is in good agreement with the calculation result of the general beam element, and the maximum error is not more than 0.6%.

Embodiment 2

[0078] Example 2: Circular Tunnel

[0079] like Figure 8 The circular tunnel shown is subjected to vertical uniform force p=100kPa up and down, horizontal force e=λp=0.5×100=50kPa to the left and right, thickness t=0.4m, outer diameter r=5.0m. The elastic modulus of the material E=2.8×10 7 kPa, Poisson's ratio μ = 0.2, excluding self-weight.

[0080] According to the general beam unit calculation, the lining internal force calculation formula is

[0081] M = pr 2 4 ( 1 - λ ) cos 2 α N = pr ( cos ...

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Abstract

A method for calculating beam unit with certain thickness includes utilizing generalized node finite-element to calculate structure displacement and stress result, treating each node as a point with arbitrarily many freedom to obtain displacement function expression of said finite element, deriving out unit stress according to said displacement function then converting stress calculation result of entity unit to be bending moment and axle force as well as shear force in engineering as per rod and beam unit theory.

Description

technical field [0001] The invention relates to a calculation method for a beam unit with thickness. Background technique [0002] At present, the calculation methods of underground structures are mainly divided into load structure method and stratum structure method. Both the load structure method and the stratum structure method can be solved by numerical methods. Currently commonly used finite element method software uses special bar-beam-plate-shell elements to simulate these structural members, but such processing still brings some troubles, such as the two-dimensional analysis of the first lining and the second lining of the tunnel. The second lining is simplified as a beam, no matter whether the center line of the first lining or the second lining or the contour line of the surrounding rock connected with the first lining is used as the calculation position of the beam, there is a larger distance compared with the actual one, and the beam-beam model Simplification w...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): E04B1/00
Inventor 蔡永昌朱合华丁文其李晓军王晓形周建晖
Owner TONGJI UNIV
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