CN103454101A - Method for obtaining torsional equivalent stiffness of skin stiffened cylindrical shell structure - Google Patents

Abstract

The invention relates to a method for obtaining the torsional equivalent stiffness of a skin stiffened cylindrical shell structure. The method comprises the following steps: step 1, the skin torsional elasticity modulus, stringer torsional elasticity modulus, skin shell diameter and skin thickness of the skin stiffened cylindrical shell structure are collected respectively, wherein collected stringers are of m categories totally, and then the number, sectional area and polar moment of inertia of the stringers in each category are collected; step 2, the sum of the polar moment of inertia of all the stringers relative to shafts of the stringers are obtained; step 3, the polar moment of inertia of skin is obtained; step 4, the total torsional equivalent stiffness of the skin stiffened cylindrical shell structure is obtained. The method for obtaining the torsional equivalent stiffness of the skin stiffened cylindrical shell structure fundamentally solves the problem that the computation of rocket torsional stiffness is too perplexing, and can be used for obtaining a more accurate torsional stiffness result.

Description

The covering Stiffened Cylindrical Shell Structure reverses the equivalent stiffness acquisition methods

Technical field

The present invention relates to a kind of torsion equivalent stiffness acquisition methods, be mainly concerned with the acquisition methods that carrier rocket and liquid missile typical case covering Stiffened Cylindrical Shell Structure reverse equivalent stiffness.

Background technology

The covering Stiffened Cylindrical Shell Structure is comprised of covering, stringer, ring frame, has high strength, rigidity, lighting characteristic, application widely in rocket structure.Wherein covering can Bending, torsion, Tensile or Compressive Loading, and stringer is as longitudinal member, its cross sectional dimensions relative length is very little, only bears the load axial along himself, bear reverse and self transverse curvature very low, can ignore.

Based on covering Stiffened Cylindrical Shell Structure dynamic modeling method, study, particularly torsional rigidity equivalent method research, set up rational covering Stiffened Cylindrical Shell Structure and reverse kinetic model, obtain rocket low order torque characteristic accurately, very crucial for the rocket development.

For the covering Stiffened Cylindrical Shell Structure, current driving force is learned modeling method three kinds:

Model 1: equivalent thickness model

This equivalence computation model is a bare hull with uniform cross-section thickness, can directly utilize equivalent thickness to calculate torsional rigidity.When calculating torsional rigidity, can be equivalent to beam to this shell.

Model 2: Varying-thickness model

In this model, the covering with vertical stringer is partly thickeied.It is that face is connected with shell that this method is equivalent to stringer, and because stringer is considered to identical and along circumferentially being uniformly distributed, so the cross section of this Varying-thickness shell while reversing still can regard plane as, there is no warpage.

Model 3: shell-beam model

In this model, simulate covering with shell unit, simulate stringer with beam element, and practical structures is more approaching.

The first model modeling is simple, and calculated amount is less, but the result that current computing method obtain is bigger than normal than actual value; Second model modeling complexity, calculated amount is larger, but result of calculation is bigger than normal equally than actual value; The third model and practical structures are more approaching, but modeling is more complicated, and calculated amount is larger, and the result and the actual value that obtain are more approaching.

Therefore, urgently provide a kind of computing method that can obtain accurately and fast covering Stiffened Cylindrical Shell Structure torsional rigidity.

Summary of the invention

The technical matters that will solve of the present invention is to provide a kind of for covering Stiffened Cylindrical Shell Structure commonly used in rocket, can accurately reflect the equivalent stiffness acquisition methods of its torsional rigidity.

In order to solve the problems of the technologies described above, technical scheme of the present invention is that a kind of covering Stiffened Cylindrical Shell Structure reverses the equivalent stiffness acquisition methods, comprises the following steps:

Step 1, gather respectively the covering modulus of torsion G of covering Stiffened Cylindrical Shell Structure _δ, stringer modulus of torsion G _b, covering shell diameter D, covering thickness δ; The stringer gathered has m class stringer, and then gathers the number N of i class stringer _i, sectional area A _biand polar moment of inertia J _bi, i=1 wherein, 2 ..., m;

The number N of the i class stringer that step 2, basis collect _iwith polar moment of inertia J _bi, by single stringer relatively the polar moment of inertia of self axle superposeed, obtain the stringer polar moment of inertia summation J of all stringers for self axle _b;

$J_b=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{N}_i{J}_{\mathrm{bi}};$

Step 3, according to the covering shell diameter D that collects, covering thickness δ, obtain the polar moment of inertia J of covering _δ;

$J_{\mathrm{\δ}}=\frac{\mathrm{\π}}{4}{D}^3\mathrm{\δ};$

Step 4, the stringer polar moment of inertia summation J obtained according to step 2 and step 3 _band the polar moment of inertia J of covering _δ, obtain the total torsion equivalent stiffness K of covering Stiffened Cylindrical Shell Structure _n;

K _N=G _δJ _δ+G _bJ _b。

The present invention has fundamentally solved puzzlement rocket torsional rigidity and has calculated a difficult problem bigger than normal, has obtained torsional rigidity result more accurately.

The accompanying drawing explanation

Fig. 1 is covering Stiffened Cylindrical Shell Structure schematic diagram involved in the present invention.

In figure: 1-covering shell, 2-stringer.

Embodiment

A kind of covering Stiffened Cylindrical Shell Structure of the present invention reverses the equivalent stiffness acquisition methods, comprises the following steps:

Step 1, gather respectively the covering modulus of torsion G of covering Stiffened Cylindrical Shell Structure _δ, stringer modulus of torsion G _b, covering shell diameter D, covering thickness δ; The stringer gathered has m class stringer, gathers the number N of i class stringer _i, polar moment of inertia J _bi, i=1 wherein, 2 ..., m;

Step 2, by single stringer relatively the polar moment of inertia of self axle superposeed, obtain the polar moment of inertia summation of all stringers for self axle

Step 3, for stressed-skin construction, polar moment of inertia because the relative D of δ is very little, therefore can ignore δ ³, the polar moment of inertia of covering

Step 4, for T-shaped, the L-type stringer that extensively adopt in rocket, its torque characteristic all is similar to Open Thin-walled Members.When Cylindrical Shell produces torsional deflection, the micro-shear stress in the stringer xsect forms micro-couple, the geometric properties thickness that the length of the arm of couple is stringer.Therefore, for the stringer structure, to the total polar moment of inertia of total, contribution does not need to consider polar moment of inertia to its polar moment of inertia moves the axle effect.

Consider covering and stringer polar moment of inertia action effect, can obtain the total torsion equivalent stiffness K of covering Stiffened Cylindrical Shell Structure _n=G _δj _δ+ G _bj _b.

Above mentioned for the covering Stiffened Cylindrical Shell Structure, three kinds of modeling methods that current driving force is learned, the first model modeling is simple, and calculated amount is less, but the result that current computing method obtain is bigger than normal than actual value; Second model modeling complexity, calculated amount is larger, but result of calculation is bigger than normal equally than actual value; The third model and practical structures are more approaching, but modeling is more complicated, and calculated amount is larger, and the result and the actual value that obtain are more or less the same.

Method of the present invention is applied to the first model, the effect that can realize that modeling is simple, calculated amount is little, result of calculation and actual value is more or less the same simultaneously.

Concrete case analysis:

With an example, demonstrate: to structure shown in Fig. 1, under fixed boundary condition, gather covering and stringer correlation parameter, the material shear modulus G _δ=G _b=26.7GPa, covering diameter D=3m, thickness δ=0.0012m, all adopting the round stringer of a class is m=1; The stringer number is N ₁=60, polar moment of inertia J _b1=5.374e-8m ³.

Be the existence function relation between the total actual torsional rigidity of covering Stiffened Cylindrical Shell Structure torsion frequency and covering Stiffened Cylindrical Shell Structure, in the engineering custom, usually adopt this frequency as analysis indexes, but they be of equal value in fact.

Under fixed boundary condition, covering Stiffened Cylindrical Shell Structure torsion frequency computing formula

$f_n=\frac{n}{2l}\sqrt{\frac{G_{\mathrm{\δ}}{J}_{\mathrm{\δ}}}{\mathrm{\ρ}(J_{\mathrm{\δ}}+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{N}_i{J}_{\mathrm{bi}})}},$ n=1，2,3,…；

In formula, ρ is density of material ρ=2800Kg/m ³, l is shell length l=51m, the order that n is frequency.Utilize quadrangular plate unit and beam element in finite element method to simulate, axially divide 200 unit, circumferentially divide 60 unit.Three kinds of the model calculation are in Table 1.

Model 1, model 2, model 3 are based on respectively now methodical equivalent thickness model, Varying-thickness model, shell-beam model, and improved model 1 is based on the equivalent thickness model of the inventive method.

The torsion frequency value that above various model calculates is in Table 1:

Table 1 torsion frequency (Hz)

As can be seen from Table 1, the frequency values that model 1 and model 2 relative models 3 calculate is bigger than normal, known according to formula, and corresponding torsional rigidity value is also bigger than normal.The frequency values that improved model 1 calculated value and model 3 calculate is basic identical, and corresponding torsional rigidity value is also basic identical.

Claims (1)

1. a covering Stiffened Cylindrical Shell Structure reverses the equivalent stiffness acquisition methods, it is characterized in that: comprise the following steps:

Step 1, gather respectively the covering modulus of torsion G of covering Stiffened Cylindrical Shell Structure _δ, stringer modulus of torsion G _b, covering shell diameter D, covering thickness δ; The stringer gathered has m class stringer, and then gathers the number N of i class stringer _i, polar moment of inertia J _bi, i=1 wherein, 2 ..., m;

The number N of the i class stringer that step 2, basis collect _iwith polar moment of inertia J _bi, by single stringer relatively the polar moment of inertia of self axle superposeed, obtain the stringer polar moment of inertia summation J of all stringers for self axle _b;

$J_b=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{N}_i{J}_{\mathrm{bi}};$

Step 3, according to the covering shell diameter D that collects, covering thickness δ, obtain the polar moment of inertia J of covering _δ;

$J_{\mathrm{\δ}}=\frac{\mathrm{\π}}{4}{D}^3\mathrm{\δ};$

Step 4, the stringer polar moment of inertia summation J obtained according to step 2 and step 3 _band the polar moment of inertia J of covering _δ, obtain the total torsion equivalent stiffness K of covering Stiffened Cylindrical Shell Structure _n;

K _N=G _δJ _δ+G _bJ _b。

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