CN111177823A - Cavity expansion theoretical calculation method suitable for brick masonry penetration - Google Patents

Abstract

The invention belongs to the field of cavity expansion theory calculation, and particularly relates to a cavity expansion theory calculation method suitable for brick masonry penetration. The method comprises the following steps: (1): obtaining the acceleration of a penetration object by a classical cavity expansion theory calculation method; (2): correcting the acceleration in the step (1): carrying out a plurality of groups of penetration tests, respectively fitting speed change curves of penetration objects with different incident speeds obtained by the tests to obtain a speed change function, and differentiating to obtain an acceleration change function; and correcting the acceleration change function obtained by the cavity expansion theory under the corresponding incident speed by using the acceleration change function to obtain a function of which the acceleration correction coefficient is independent of the incident speed. According to the invention, the acceleration function obtained by the test is used for correcting the acceleration obtained by the classic cavity expansion theory, so that the classic cavity expansion theory is suitable for the penetration of the brick masonry.

Description

Cavity expansion theoretical calculation method suitable for brick masonry penetration

Technical Field

The invention belongs to the field of cavity expansion theory calculation, and particularly relates to a cavity expansion theory calculation method suitable for brick masonry penetration.

Background

The cavity expansion theory is mathematical description of the object penetration process, the material parameters of the penetration object and the target body are known, and the stress of any point on the surface of the penetration object at any speed can be obtained through the cavity expansion theory, so that the total resistance of the penetration object at any speed is obtained, the acceleration of the penetration object at any speed is obtained, and finally the motion equation of the penetration object is obtained.

The existing cavity expansion theory calculation method is established based on the constitutive equation of concrete, the concrete and the brick masonry are both brittle materials for construction, but compared with the concrete, the brick masonry is an integral material built by bricks and mortar, the material has more pores, and compared with the integrity of the concrete, the brick masonry is a dispersive structure. Therefore, the calculation method of the cavity expansion theory cannot be directly applied to the penetration of the brick masonry, and the research of the cavity expansion theory applied to the brick masonry is not available at home and abroad. On the other hand, the existing cavity expansion theory idealizes a penetration object into a rigid body, a certain error is generated, the penetration result cannot be accurately predicted, and the application of the cavity expansion theory in penetration brick masonry is limited.

Disclosure of Invention

The invention aims to provide a cavity expansion theory calculation method suitable for brick masonry penetration.

The technical solution for realizing the purpose of the invention is as follows: a cavity expansion theory calculation method suitable for brick masonry penetration comprises the following steps:

step (1): obtaining the acceleration of a penetration object by a classical cavity expansion theory calculation method;

step (2): correcting the acceleration in the step (1):

carrying out a plurality of groups of penetration tests, respectively fitting speed change curves of penetration objects with different incident speeds obtained by the tests to obtain a speed change function, and differentiating to obtain an acceleration change function;

and correcting the acceleration change function obtained by the cavity expansion theory under the corresponding incident speed by using the tested acceleration change function, fitting the acceleration correction coefficients of penetration objects with different incident speeds by taking the initial speed as an independent variable, and obtaining a function of the acceleration correction coefficient by taking the incident speed as the independent variable, thereby obtaining the correction formula of the acceleration.

Further, the acceleration correction formula in step (2) is as follows:

let the acceleration of the penetrating object before correction be a₁The unit is m/s ^ 2; the corrected acceleration of the penetration object is a₂The unit is m/s ^ 2; y is the incident velocity, in m/s, then:

a₂＝c₁a₁-c₂

wherein c is₁And c₂Obtaining a plurality of groups of acceleration change functions a under different incident speeds by tests and a classical cavity expansion theory for fitting the solved coefficients₁And a₂Thereby obtaining a plurality of groups of correction coefficients c₁And c₂For a plurality of groups c₁And c₂C obtained by fitting the incident speed y as an independent variable₁And c₂The expression for the incident speed y is:

c₁＝-1.17227×10^-4y³+0.28418y²-229.58378y+61809.6

c₂＝-4.7201×10^-5y³+0.11256y²-89.4088y+23650.8

compared with the prior art, the invention has the remarkable advantages that:

(1) according to the invention, the acceleration function obtained by the test is used for correcting the acceleration obtained by the classic cavity expansion theory, so that the classic cavity expansion theory is suitable for the penetration of the brick masonry, and the blank of research is filled;

(2) the invention corrects the acceleration by using the test data, makes up the error caused by the fact that the cavity expansion theory idealizes the penetration object into the rigid body, and is more accurate.

Detailed Description

The invention will now be further illustrated with reference to specific examples.

And (3) before the step of correcting the acceleration, determining the cavity surface radial stress of the penetration object at a given speed by using a common cavity expansion theory calculation method through an iterative method, thereby obtaining the theoretical acceleration of the penetration object. The acceleration of the penetrating object is then corrected using the test data.

The cavity expansion theory calculation method based on test correction and suitable for brick masonry penetration comprises the following steps:

step 1, obtaining the acceleration of a penetration object by a classical cavity expansion theory calculation method.

Step 2, correcting acceleration: and respectively fitting the speed change curves of the penetration objects with different incident speeds obtained by the test to obtain a speed change function, and differentiating to obtain an acceleration change function. And correcting the acceleration change function obtained by the cavity expansion theory under the corresponding incident speed by using the tested acceleration change function, fitting the acceleration correction coefficients of penetration objects with different incident speeds by taking the incident speed as an independent variable, and obtaining the function of the acceleration correction coefficient by taking the incident speed as the independent variable, thereby obtaining the correction formula of the acceleration.

Let the acceleration of the penetrating object before correction be a₁The unit is m/s ^ 2; the corrected acceleration of the penetration object is a₂The unit is m/s ^ 2; y is the incident velocity, in m/s, then:

a₂＝c₁a₁-c₂

wherein c is₁And c₂The coefficients to be solved for the fit. Obtaining 10 groups of acceleration change functions a under different incident speeds through experiments and the classical cavity expansion theory₁And a₂Thereby obtaining 10 sets of correction coefficients c₁And c₂. For 10 groups c₁And c₂C obtained by fitting the incident speed y as an independent variable₁And c₂The expression for the incident speed y is:

c₁＝-1.17227×10^-4y³+0.28418y²-229.58378y+61809.6

c₂＝-4.7201×10^-5y³+0.11256y²-89.4088y+23650.8

according to the method, the acceleration function obtained through the test corrects the acceleration obtained by the classic cavity expansion theory, the difference caused by the constitutive equation of the concrete and the brick masonry is made up, the classic cavity expansion theory is suitable for brick masonry penetration, the acceleration of a penetration object can be rapidly obtained, and therefore the brick masonry penetration result is predicted. Meanwhile, through test correction, the method comprises the influence of the deformation of the penetration object on the acceleration, makes up for the error caused by the fact that the penetration object is idealized into a rigid body by a cavity expansion theory, and can predict the penetration result of the brick masonry more accurately.

Claims (2)

1. A cavity expansion theory calculation method suitable for brick masonry penetration is characterized by comprising the following steps:

step (1): obtaining the acceleration of a penetration object by a classical cavity expansion theory calculation method;

step (2): correcting the acceleration in the step (1):

carrying out a plurality of groups of penetration tests, respectively fitting speed change curves of penetration objects with different incident speeds obtained by the tests to obtain a speed change function, and differentiating to obtain an acceleration change function;

and correcting the acceleration change function obtained by the cavity expansion theory under the corresponding incident speed by using the tested acceleration change function, fitting the acceleration correction coefficients of penetration objects with different incident speeds by taking the initial speed as an independent variable, and obtaining a function of the acceleration correction coefficient by taking the incident speed as the independent variable, thereby obtaining the correction formula of the acceleration.

2. The method of claim 1, wherein the step (2) of correcting the acceleration is represented by the following formula:

let the acceleration of the penetrating object before correction be a₁The unit is m/s ^ 2; the corrected acceleration of the penetration object is a₂The unit is m/s ^ 2; y is the incident velocity, in m/s, then:

a₂＝c₁a₁-c₂

wherein c is₁And c₂Obtaining a plurality of groups of acceleration change functions a under different incident speeds by tests and a classical cavity expansion theory for fitting the solved coefficients₁And a₂Thereby obtaining a plurality of groups of correction coefficients c₁And c₂For a plurality of groups c₁And c₂C obtained by fitting the incident speed y as an independent variable₁And c₂The expression for the incident speed y is:

c₁＝-1.17227×10^-4y³+0.28418y²-229.58378y+61809.6

c₂＝-4.7201×10^-5y³+0.11256y²-89.4088y+23650.8。