[go: up one dir, main page]

CN110990921A - An Improved Interval Truncation Method for Cantilever Beam Safety Design - Google Patents

An Improved Interval Truncation Method for Cantilever Beam Safety Design Download PDF

Info

Publication number
CN110990921A
CN110990921A CN201911178412.3A CN201911178412A CN110990921A CN 110990921 A CN110990921 A CN 110990921A CN 201911178412 A CN201911178412 A CN 201911178412A CN 110990921 A CN110990921 A CN 110990921A
Authority
CN
China
Prior art keywords
interval
value
deflection
truncation
cantilever beam
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201911178412.3A
Other languages
Chinese (zh)
Other versions
CN110990921B (en
Inventor
刘新田
张玉茹
喻学广
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shanghai University of Engineering Science
Original Assignee
Shanghai University of Engineering Science
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shanghai University of Engineering Science filed Critical Shanghai University of Engineering Science
Priority to CN201911178412.3A priority Critical patent/CN110990921B/en
Publication of CN110990921A publication Critical patent/CN110990921A/en
Application granted granted Critical
Publication of CN110990921B publication Critical patent/CN110990921B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)

Abstract

The invention relates to an improved interval truncation method for cantilever beam safety design, which comprises the steps of firstly determining an independent variable and a value or a value interval thereof, obtaining a function relation formula for solving deflection according to material mechanics knowledge, then analyzing and processing the function relation formula to obtain a correlation independent variable, then uniformly dividing the value interval with the correlation independent variable into n subintervals, solving the deflection by using a subinterval truncation criterion function solving formula, and finally judging whether the deflection exceeds an allowable deflection interval; the subinterval truncation criterion function f (x) solves the following:
Figure DDA0002290617910000011
wherein X is the value interval of the independent variable with correlation,
Figure DDA0002290617910000012
is the central value of the nth segment of the sub-interval,
Figure DDA0002290617910000013
is f (X) in
Figure DDA0002290617910000014
Function value of (X)cIs the central value, f' (X), of the overall interval Xc) Is f (X) at XcValue of the first derivative of (d), Δ XiIs the interval width of the ith sub-interval, and e is the truncation factor of the sub-interval. The method can effectively inhibit the expansion problem of the cantilever beam deflection interval, so that the cantilever beam deflection design meets the actual requirements of engineering structures, and is safe and reliable.

Description

Improved interval truncation method for cantilever beam safety design
Technical Field
The invention belongs to the technical field of engineering structure safety, and relates to an improved interval truncation method for cantilever beam safety design.
Background
In practical engineering problems, some uncertainty factors are always encountered. In most cases, structural material parameters, geometric parameters and external forces are virtually uncertain due to factors such as measurement inaccuracies, limitations in construction levels and conditions, and the like. Most of output results adopted by the prior art are output result calculation based on an ideal value, and because input variables have uncertainty, the output result is also uncertain, namely, output parameters have upper and lower error range values based on the ideal value, when similar problems are processed by using a basic interval algorithm, the obtained result is an accurate solution when the interval parameters are mutually independent, but when interval functions have monotonicity and correlation, the result deviation obtained by using the basic interval algorithm is very large, so that the interval of the output result is expanded, the result interval is possibly enlarged during engineering structure calculation and judgment, the credible interval is not accurate enough, the engineering structure is unstable, and finally the engineering structure is unsafe.
Therefore, how to restrain the expansion of the output parameter interval to enable the output range to be more accurate and effective becomes a key problem of ensuring the safety of the engineering structure.
Disclosure of Invention
The invention aims to solve the problems that in the prior art, the basic algorithm in the actual engineering structure can expand the interval of the operation result to cause inaccurate credible interval and unstable engineering structure, and provides an improved interval truncation method for cantilever beam safety design.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an improved interval truncation method for cantilever beam safety design includes determining independent variable and its value or value interval, and based on material mechanicsObtaining a function relation formula for solving the deflection by knowledge, and analyzing the function relation formula for solving the deflection to obtain independent variables with correlation (the correlation of the variables specifically refers to the correlation of more than two variables, and the correlation of two or more interval variables refers to that the two or more interval variables contain the same interval number component, such as the known interval number x1Let y1＝x1，y2＝x1-1, the number of intervals y1And y2Is relevant), then the value interval with the relevant independent variable is evenly divided into n subintervals, the subinterval truncation criterion function is used for solving the deflection by using a formula, and finally whether the deflection exceeds the allowable deflection interval is judged, and if not, the safety is realized; otherwise, it is unsafe;
the subinterval truncation criterion function f (x) solves the following:
Figure BDA0002290617890000011
wherein X is the value interval of the independent variable with correlation,
Figure BDA0002290617890000012
is the central value of the nth segment of the sub-interval,
Figure BDA0002290617890000013
is f (X) in
Figure BDA0002290617890000014
Function value of (X)cIs the central value, f' (X), of the overall interval Xc) Is f (X) at XcValue of the first derivative of (d), Δ XiIs the interval width of the ith sub-interval, e is the truncation factor (uncertainty interval) of the sub-interval, e [ -1,0 [ ]]N is a subinterval order number, i is 1,2, n is 2mThe value of m is obtained by the for loop iteration of the program, and the termination condition of the iteration is that the value range of f (X) is not changed any more;
number of defined intervals
Figure BDA0002290617890000021
The central value of the whole interval
Figure BDA0002290617890000022
Width of interval
Figure BDA0002290617890000023
In order to inhibit the interval correlation, the invention evenly divides the interval number X of the parameter into n small sub-intervals, and provides a truncation criterion based on the sub-intervals:
Figure BDA0002290617890000024
the width of each subinterval is:
Figure BDA0002290617890000025
the central value of each subinterval is:
Figure BDA0002290617890000026
with the increase of n, X belongs to X for any X ∈ XiCorrespondingly, let X belong to Xi,f(x)∈f(X)；
Firstly, carrying out correlation analysis on a function containing correlation variables, uniformly dividing an interval with the correlation variables into n small sub-intervals, and finally solving an output variable interval of the function by using a sub-interval truncation rule function solving formula based on an nth sub-interval average value and an integral interval average value; according to the invention, the correlation of the interval parameters is reduced by changing the function expression form of the interval parameters, so that the reliability of the obtained output variable interval is more accurate and reasonable, and the cantilever beam design is safe and reliable.
As a preferred technical scheme:
in the above-mentioned improved interval truncation method for cantilever beam safety design, the confidence of the solution obtained by the subinterval truncation criterion function is R, and the real value range of f (X) is
Figure BDA0002290617890000027
The solution obtained by using a subinterval truncation criterion function is
Figure BDA0002290617890000028
If it is not
Figure BDA0002290617890000029
and
Figure BDA00022906178900000210
R is 0.99, and the reliability is high; otherwise, R is 0, and reliability is low.
An improved interval truncation method for cantilever beam safety design as described above, the independent variables comprising: length L in mm, modulus of elasticity E in GN/m2The section moment of inertia I in mm4The couple M is in the unit of N.mm, and the distance a between the couple and the fixed end is in the unit of mm.
The improved interval truncation method for cantilever beam safety design comprises the following steps of:
Figure BDA00022906178900000211
an improved interval truncation method for cantilever beam safety design as described above has a correlation argument a.
Has the advantages that:
(1) the improved interval truncation method for cantilever beam safety design is simple, convenient and fast and has strong feasibility;
(2) the improved interval truncation method for cantilever beam safety design can effectively inhibit the expansion problem of the cantilever beam deflection interval, so that the cantilever beam deflection design meets the actual requirements of engineering structures, and is safe and reliable.
Drawings
FIG. 1 is a schematic view of a cantilever beam.
Detailed Description
The invention will be further illustrated with reference to specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
An improved interval truncation method for cantilever beam safety design is provided, wherein a schematic diagram of a cantilever beam is shown in figure 1, and the specific process is as follows:
(1) determining an independent variable and a value or a value interval thereof, wherein the independent variable comprises: length L in mm, modulus of elasticity E in GN/m2The section moment of inertia I in mm4The couple M is in the unit of N.mm, the distance a between the couple and the fixed end is in the unit of mm, L is 300mm, and E is 200GN/M2，I＝200mm4，M＝[2000,5000]N·mm，a＝[150,250]mm；
(2) Obtaining a function relation formula for solving the deflection according to the knowledge of the material mechanics, which is as follows:
Figure BDA0002290617890000031
(3) analyzing and processing the function relation for solving the deflection to obtain an independent variable with correlation, namely a;
(4) uniformly dividing a into n-212Small sub-interval, i-th sub-interval
Figure BDA0002290617890000032
The width of each subinterval is:
Figure BDA0002290617890000033
the central value of each subinterval is:
Figure BDA0002290617890000034
and solving the deflection by using a subinterval truncation criterion function solving formula, wherein the subinterval truncation criterion function f (X) solves the formula as follows:
Figure BDA0002290617890000035
in the formula, X is a value interval of a,
Figure BDA0002290617890000036
is the central value of the nth segment of the sub-interval,
Figure BDA0002290617890000037
is f (X) in
Figure BDA0002290617890000038
Function value of (X)cIs the central value, f' (X), of the overall interval Xc) Is f (X) at XcValue of the first derivative of (d), Δ XiIs the interval width of the ith sub-interval, e is the truncation factor of the sub-interval, e [ -1,0 [ ]]N is a subinterval order number, i is 1,2, n is 2mThe value of m is obtained by the for loop iteration of the program, and the termination condition of the iteration is that the value range of f (X) is not changed any more;
the confidence of the solution obtained by the subinterval truncation criterion function is R, f (X) and the real value range is
Figure BDA0002290617890000041
The solution obtained by using a subinterval truncation criterion function is
Figure BDA0002290617890000042
If it is not
Figure BDA0002290617890000043
and
Figure BDA0002290617890000044
R is 0.99, and the reliability is high; otherwise, R is 0, so that the reliability is low;
the output deflection interval obtained by the result obtained by MATALAB software is [0.00156247, 0.00546867] m;
performing interval calculation (namely analyzing monotonicity of a function, performing interval operation according to a monotonous interval, and finally combining output result intervals) by a combination method to obtain a deflection interval true value range of the test of [0.00168750, 0.00546875] m;
calculating the reliability of the deflection interval obtained by the deflection interval real value domain and the improved interval truncation algorithm:
Figure BDA0002290617890000045
and
Figure BDA0002290617890000046
r is 0.99, which indicates that the reliability of the solution result of the subinterval truncation criterion function is high;
(4) judging whether the deflection exceeds the allowable deflection interval, if not, the method is safe; otherwise, the method is unsafe, the allowable deflection interval in the experiment is [0.0015, 0.01] m, and the obtained intervals are compared to know that the interval calculated by the improved interval truncation method for cantilever beam safety design is within the allowable deflection interval range and the interval radius of the interval relative to the real value domain is expanded by 1.033 times; calculating according to a function relation formula of solving deflection of material mechanics, wherein the obtained deflection interval is [0.00131260, 0.00703125] m; the interval is not only outside the range of the allowable deflection interval, but also is expanded by 1.512 times relative to the interval of the real value range; the improved interval truncation method for cantilever beam safety design can effectively inhibit the expansion problem of the cantilever beam deflection interval, so that the cantilever beam deflection design meets the actual requirements of engineering structures, and is safe and reliable.

Claims (5)

1.一种用于悬臂梁安全设计的改进区间截断方法，其特征是：首先确定自变量及其取值或取值区间，根据材料力学知识得出求解挠度的函数关系式，然后对求解挠度的函数关系式进行分析处理得到具有相关性自变量，接着将具有相关性自变量的取值区间均匀地划分为n个子区间，运用子区间截断准则函数求解公式求解挠度，最后判断挠度是否超出许用挠度区间，如果否，则安全；反之，则不安全；1. An improved interval truncation method for the safety design of a cantilever beam, characterized in that: first determine the independent variable and its value or value interval, obtain a functional relationship for solving deflection according to the knowledge of material mechanics, and then calculate the deflection for solving Then, the value interval of the correlated independent variables is evenly divided into n sub-intervals, and the sub-interval truncation criterion function is used to solve the formula to solve the deflection, and finally it is judged whether the deflection exceeds the allowable range. Use the deflection interval, if not, it is safe; otherwise, it is not safe; 子区间截断准则函数f(X)求解公式如下：The formula for solving the subinterval truncation criterion function f(X) is as follows:
Figure FDA0002290617880000011
Figure FDA0002290617880000011
 式中，X为具有相关性自变量的取值区间，
Figure FDA0002290617880000012
是第n段子区间的中心值，
Figure FDA0002290617880000013
为f(X)在
Figure FDA0002290617880000014
处的函数值，Xc为整体区间X的中心值，f′(Xc)是f(X)在Xc处的一阶导数值，ΔXi是第i个子区间的区间宽度，e为子区间的截断因子，e＝[-1,0]，i＝1,2,...n为子区间顺序数，n＝2m，m的取值是通过程序的for循环迭代得到的，迭代的终止条件为f(X)的值域不再变化。In the formula, X is the value interval of the independent variable with correlation,
Figure FDA0002290617880000012
is the center value of the nth subinterval,
Figure FDA0002290617880000013
for f(X) at
Figure FDA0002290617880000014
The function value at , X c is the central value of the overall interval X, f'(X c ) is the first derivative value of f(X) at X c , ΔX i is the interval width of the ith sub-interval, and e is the sub-interval The truncation factor of the interval, e=[-1,0], i=1,2,...n is the sequence number of the sub-interval, n=2 m , the value of m is obtained through the iteration of the for loop of the program. The termination condition is that the range of f(X) no longer changes. 2.根据权利要求1所述的一种用于悬臂梁安全设计的改进区间截断方法，其特征在于，子区间截断准则函数求得的解的可信度为R，f(X)的真实值域为
Figure FDA0002290617880000015
采用子区间截断准则函数求得的解为
Figure FDA0002290617880000016
如果
Figure FDA0002290617880000017
则R＝0.99，可信度高；反之，R＝0，可信度低。2. a kind of improved interval truncation method for cantilever beam safety design according to claim 1, is characterized in that, the credibility of the solution that subinterval truncation criterion function obtains is R, the true value of f(X) Domain is
Figure FDA0002290617880000015
The solution obtained using the subinterval truncation criterion function is
Figure FDA0002290617880000016
if
Figure FDA0002290617880000017
Then R=0.99, the reliability is high; otherwise, R=0, the reliability is low. 3.根据权利要求1所述的一种用于悬臂梁安全设计的改进区间截断方法，其特征在于，自变量包括：长度L，单位为mm，弹性模量E，单位为GN/m2，截面惯性矩I，单位为mm4，力偶M，单位为N·mm，力偶与固定端之间的距离a，单位为mm。3. A kind of improved interval truncation method for cantilever beam safety design according to claim 1, is characterized in that, independent variable comprises: length L, unit is mm, elastic modulus E, unit is GN/m 2 , The moment of inertia I of the section is in mm 4 , the force couple M is in N·mm, and the distance a between the force couple and the fixed end is in mm. 4.根据权利要求3所述的一种用于悬臂梁安全设计的改进区间截断方法，其特征在于，求解挠度的函数关系式如下：4. a kind of improved interval truncation method for cantilever beam safety design according to claim 3, is characterized in that, the functional relation of solving deflection is as follows:
Figure FDA0002290617880000018
Figure FDA0002290617880000018
 5.根据权利要求4所述的一种用于悬臂梁安全设计的改进区间截断方法，其特征在于，具有相关性自变量为a。5 . The improved interval truncation method for cantilever beam safety design according to claim 4 , wherein the independent variable with correlation is a. 6 .
CN201911178412.3A 2019-11-27 2019-11-27 Improved interval truncation method for cantilever beam safety design Active CN110990921B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911178412.3A CN110990921B (en) 2019-11-27 2019-11-27 Improved interval truncation method for cantilever beam safety design

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911178412.3A CN110990921B (en) 2019-11-27 2019-11-27 Improved interval truncation method for cantilever beam safety design

Publications (2)

Publication Number Publication Date
CN110990921A true CN110990921A (en) 2020-04-10
CN110990921B CN110990921B (en) 2023-04-18

Family

ID=70087406

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911178412.3A Active CN110990921B (en) 2019-11-27 2019-11-27 Improved interval truncation method for cantilever beam safety design

Country Status (1)

Country Link
CN (1) CN110990921B (en)

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030172095A1 (en) * 2002-03-11 2003-09-11 Walster G. William Method and apparatus solving problems having interval parameters
CN103455689A (en) * 2013-09-18 2013-12-18 福州大学 Interval model correcting method based on Taylor series expansion
CN105022921A (en) * 2015-07-14 2015-11-04 福州大学 Fuzzy system reliability design method in combination with modal interval algorithm
CN105893698A (en) * 2016-04-25 2016-08-24 华东交通大学 Affinity algorithm for solving non-probability reliability index of structural engineering
CN108563895A (en) * 2018-04-24 2018-09-21 湖南大学 A kind of interval model modification method considering correlation
CN110334425A (en) * 2019-06-26 2019-10-15 上海工程技术大学 An Improved Interval Algorithm for Engineering Structure Uncertainty

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030172095A1 (en) * 2002-03-11 2003-09-11 Walster G. William Method and apparatus solving problems having interval parameters
CN103455689A (en) * 2013-09-18 2013-12-18 福州大学 Interval model correcting method based on Taylor series expansion
CN105022921A (en) * 2015-07-14 2015-11-04 福州大学 Fuzzy system reliability design method in combination with modal interval algorithm
CN105893698A (en) * 2016-04-25 2016-08-24 华东交通大学 Affinity algorithm for solving non-probability reliability index of structural engineering
CN108563895A (en) * 2018-04-24 2018-09-21 湖南大学 A kind of interval model modification method considering correlation
CN110334425A (en) * 2019-06-26 2019-10-15 上海工程技术大学 An Improved Interval Algorithm for Engineering Structure Uncertainty

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
常芳等: "含区间参数大挠度弯曲梁的变形计算问题", 《机械强度》 *
苏永华等: "基于区间变量的响应面可靠性分析方法", 《岩土工程学报》 *

Also Published As

Publication number Publication date
CN110990921B (en) 2023-04-18

Similar Documents

Publication Publication Date Title
CN109255173B (en) Interval Calculation Method of Structural Failure Probability Considering Interval Uncertainty
CN106650221B (en) Enhance bridge health monitoring structural response and the convergent method of temperature data correlation
Agmell et al. The link between plasticity parameters and process parameters in orthogonal cutting
CN114239175A (en) High-temperature structural member service life prediction method based on nonlinear creep-fatigue interaction
Pichler et al. Highly resolved LES of a linear HPT vane cascade using structured and unstructured codes
Zeng et al. A comprehensive empirical equation for the hydrodynamic damping of vibrating blade-like structures
CN110736400A (en) underwater drilling blasting vibration velocity calculation method considering rock internal structure
CN113177325A (en) Method and device for correcting adjustable parameters of standard k-epsilon model under complex terrain and storage medium
CN111983035A (en) Rock sample damage prediction method based on acoustic emission technology
CN105675320B (en) A kind of mechanical system running status method for real-time monitoring based on acoustic signal analysis
CN113807028A (en) Optimization method and optimization system for epoxy resin curing process
Newman Jr et al. Fatigue and crack growth in 7050-T7451 aluminum alloy under constant-and variable-amplitude loading
CN118094995A (en) Method for researching dynamic response index of concrete arch dam structure affected by earthquake intensity
CN110990921A (en) An Improved Interval Truncation Method for Cantilever Beam Safety Design
CN106442727B (en) A method and system for identifying mechanical property parameters of hard coating materials
Huang et al. Aerothermal performance robustness and reliability analysis of turbine blade squealer tip with film cooling
JP2023000306A (en) Prediction device, production equipment, and prediction method
CN102346809A (en) Method for converting blasting-vibration acceleration into velocity
CN118706958A (en) A performance evaluation method for concrete-filled steel tube components used in waste incineration power generation
CN110412312B (en) A Calculation Method for Vertical Distribution of Inrush Velocity
CN118536404A (en) Amplitude-variable load fatigue crack propagation prediction method based on dynamic Bayesian updating
CN111080020A (en) Robustness assessment method and device for drilling arrangement
CN114444344B (en) A temperature field calculation method, device, electronic device and storage medium thereof
CN118332941A (en) A method for determining the wind load shape coefficient of a structure based on force measurement wind tunnel test
CN116911085A (en) Wind-resistant reliability evaluation method and system for multiple components of long and short leg power transmission tower structure

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant