CN106777741A - A kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis - Google Patents

Abstract

The present invention provides a kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis, comprises the following steps：1) " paving " treatment is carried out to the rib rigidity in stiffened cylindrical shell；2) according to laminated shell theory, the tension and compression rigidity of rib is calculated；3) grid Stiffened Cylindrical Shells Under External Pressure rib/covering mass ratio, vertical, horizontal equivalent thickness are drawn by tension and compression Rigidity Calculation formula；4) internal pressure strength of stiffened cylindrical shell is calculated.The present invention is applied to various grid configuration structures, and the internal pressure strength design under pure internal pressure and axle pressure, moment of flexure, the effect of internal pressure connected load is calculated, and obtains its ultimate bearing capacity；Method is more visual and clear, succinct convenience, is conducive to improving grid reinforced structure bearing capacity, mitigates construction weight, realizes the accurate quick design of intensity.

Description

A kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis

Technical field

The present invention provides a kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis, is applied to various grids Accurately quickly design is calculated Stiffened Cylindrical Shell Structure internal pressure strength.

Background technology

Compared with light barrel shell, because designability is strong, the features such as load-carrying efficiency is high, stiffened cylindrical shell structure type is wide It is general to hold the ironed wall construction of axle for all kinds of.In addition to axial compressive strength and stability, internal pressure strength is also often grid reinforcement post shell One of major design operating mode.Calculating grid reinforcement post shell internal pressure strength at present mainly has engineering simplification computational methods and finite element Two kinds of analysis method.Ignore the contribution of rib in grid reinforcement pole-shell structure in traditional engineering simplification computational methods, and only examine Consider the bearing capacity of covering, cause that internal pressure strength surplus is larger, structural bearing is less efficient, is unfavorable for loss of weight.Finite element method Then need to carry out grid reinforcement post shell finite element modeling analysis, computational efficiency is relatively low.

Because method is general, and can accurately consider the influence of coupling between bending and extension, it is general using based on axisymmetrical laminated shell reason in engineering The orthotropy cylinder cover calculating method for stability of opinion carries out grid reinforcement columella, stability of external pressure design, theoretical and real This method of proof is trampled with precision higher, but lacks grid reinforcement pole-shell structure Strength co-mputation side under corresponding inner pressuring load Method.The present invention is further derived the lower grid reinforcement post shell stress intensity of inner pressuring load effect based on ripe laminated shell theory Computational methods, specify that contribution of the mesh parameter to structure internal pressure bearing capacity, and using finite element method to different grid-shapeds Formula, difference rib/covering mass ratio (m_b) structure stress and ultimate bearing capacity calculated, by comparative analysis verify The versatility and accurate reliability of this method.Result shows that the method is correctly reliable, can be used for grid reinforcement as analytic method The accurate quick design of post shell internal pressure strength is calculated, and is solved the quick careful design of grid reinforcement pole-shell structure internal pressure strength and is calculated Problem.

The content of the invention

In view of the shortcomings of the prior art, the present invention provides a kind of calculating of stiffened cylindrical shell internal pressure strength accurate Analysis Method, it can be considered that contribution of the rib to grid reinforcement pole-shell structure internal pressure bearing capacity, theory deduction goes out grid reinforcement post shell Internal pressure strength Analytic Calculation Method, realizes the accurate quick calculating to grid Stiffened Cylindrical Shells Under External Pressure internal pressure strength.

In order to achieve the above object, the technical scheme is that：

A kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis, comprise the following steps：

The first step, " paving " treatment is carried out to the rib in stiffened cylindrical shell

By rib by etc. rigidity " paving " treatment, the rib of same angle is equivalent to one layer of equivalent " orthogonal " anisotropy Layer, grid stiffening part just can change into the Orthotropic Laminates being made up of the grid rib " layer " of different angles.

If it is t that the angle of rib and housing axis is θ, width_w, rib spacing be b_s, material along rib direction springform It is E to measure, then the rib of same angle constitutes monovalent orthotropy layer.The equivalent orthotropy layer deflection be The angle theta of rib and housing axis, it is equivalent that elastic constant presses formula (1)：

Wherein, b_sIt is rib spacing；E₁It is longitudinal modulus of elasticity, E₂It is transverse modulus of elasticity, ν₁₂It is main Poisson's ratio, G₁₂For Longitudinal-transverse shear modulus, subscript 1,2 is material direction；t_wAIt is the equivalent width of rib fillet, is calculated by formula (2)：

Wherein, r is rib radius of corner；H be rib highly.

Second step, calculates the tension and compression rigidity of rib

According to laminated shell theory, the tension and compression rigidity A of Orthotropic Laminates_ijCalculated by formula (3)：

Wherein, n is the number of plies；z_k、z_k-1It is the coordinate on the upper and lower surface of kth layer；To be transformed into the rigidity of structure principal direction Element, referred to as off-axis rigidity, its subscript 1 be housing axially, 2 be housing ring, 3 directions according to right-handed coordinate system determine, 6 be around The rotation direction of 3 axles.

Off-axis rigidity is converted to by formula (4) by positive axis rigidity：

Wherein, Q_ijIt is the rigidity element of laminated material principal direction, referred to as positive axis rigidity, its subscript 1 is material principal direction (material The big direction of material mechanical performance, also known as longitudinal direction), 2 be material laterally, 3 directions determine according to right-handed coordinate system, 6 is turning around 3 axles Dynamic direction.

Positive axis rigidity is pressed formula (5) and is calculated by elastic properties of materials constant：

The positive axis rigidity that formula (1) substitution formula (5) can obtain every layer of rib equivalent layer is shown in into formula (6)：

3rd step, calculates stiffened cylindrical shell vertical, horizontal equivalent thickness

Rib vertical, horizontal tension and compression rigidity A is obtained by formula (3)₁₁、A₂₂After can draw grid Stiffened Cylindrical Shells Under External Pressure rib/covering quality Compare m_b, vertical, horizontal equivalent thickness t_dx、t_dyPrecise calculation (7)：

Wherein, t_sIt is skin thickness；M is the rib angle number for constituting grid.

4th step, calculates the internal pressure strength of stiffened cylindrical shell

4.1) Stress calculation under internal pressure effect

To stiffened cylindrical shell containing end socket, the axial stress σ under inner pressuring load P effects_x, circumference stress σ_yCalculating it is public Formula is respectively：

In formula, R is stiffened cylindrical shell housing radius.

To the stiffened cylindrical shell without end socket, there is axial stress σ_x=0.

4.2) Strength Failure criterion

It is general in engineering to use the 3rd strength theory (maximum shear stress failure criteria) to holding interior laminated structure, i.e.,

σ₁-σ₃≤σ_b (9)

Wherein, σ₁First principal stress is the circumference stress that internal pressure is producedσ₃It is third principal stress.

4.3) axle pressure is calculated with the internal pressure strength under internal pressure synergy

Axle is pressed and is with the equivalent axle compressive load under the effect of end socket internal pressure connected load：T_zh=T- π R²P_F, wherein, T is maximum Axle pressure under internal pressure design conditions, P_FIt is grid reinforcement post shell front head pressure.

Work as T_zhWhen≤0, third principal stress σ₃=0.By σ₁、σ₃Substituting into formula (9) can obtain the internal pressure pole of stiffened cylindrical shell Limiting bearing capacity is：

Work as T_zhDuring ＞ 0, third principal stress is the axial compression stress that axle pressure is producedBy σ₁、σ₃Substitute into formula (9) the internal pressure ultimate bearing capacity that can obtain stiffened cylindrical shell is：Described grid Stiffened Cylindrical The internal pressure ultimate bearing capacity of shell is the internal pressure strength of stiffened cylindrical shell.

Beneficial effects of the present invention are：The present invention provides a kind of essence for the design of complex mesh stiffening shell internal pressure strength True Analytic Calculation Method, it is adaptable under various grid configuration structures, pure internal pressure and axle pressure, moment of flexure, the effect of internal pressure connected load Internal pressure strength design calculate, obtain its ultimate bearing capacity.The method is more more visual and clear than finite element method, succinct side Just, only consider that the method that covering carrying is acted on is more accurate than former, be conducive to improving grid reinforced structure bearing capacity, mitigate knot Structure weight, realizes the accurate quick design of intensity.

Brief description of the drawings

Fig. 1 is Orthotropic Laminates schematic diagram and coordinate；

Fig. 2 (a) is just to put orthogonal 0 °/90 ° of mesh parameter schematic diagram；

Fig. 2 (b) is tilting orthogonal ± 45 ° of mesh parameter schematic diagram；

Fig. 2 (c) is the mesh parameter schematic diagram of equilateral triangle ± 30 °/90 °；

Fig. 2 (d) is the mesh parameter schematic diagram of 0 ° of equilateral triangle/± 60 °；

Fig. 2 (e) is the sectional view of the line A-A along Fig. 2 (a), Fig. 2 (b), Fig. 2 (c), Fig. 2 (d).

Specific embodiment

For make present invention solves the technical problem that, the technical scheme that uses and the technique effect that reaches it is clearer, below The present invention is described in further detail in conjunction with the accompanying drawings and embodiments.It is understood that specific implementation described herein Example is used only for explaining the present invention, rather than limitation of the invention.It also should be noted that, for the ease of description, accompanying drawing In illustrate only part rather than full content related to the present invention.

If structure is uniform grid Cylindrical Shell, input condition, including herein below are obtained：

1) grid ring-stiffened shell radius is R, is made up of the rib and covering of m kind angles, and rib angle is 0 °, 90 °, ± θ Or its combination；

2) rib parameter is wallboard thickness H, covering thickness t_s, rib spacing b_s, rib width t_w, rib height h=H-t_s, muscle Bar radius of corner r；

3) mechanical property of materials is elastic modulus E, ultimate strength σ_b；

4) load-up condition is axle pressure T, front head pressure P_F。

A kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis, i.e. structure internal pressure ultimate bearing capacity meter Calculate step as follows：

1) by rib by etc. rigidity " paving " treatment.The rib of same angle is equivalent to one layer of " orthogonal " opposite sex of equivalent Layer, grid stiffening part changes into the orthotropy layer being made up of the grid rib " layer " of different angles as shown in Figure 1 Plywood.Rib fillet equivalent width is calculated according to formula (2).

2) Fig. 2 (a), Fig. 2 (b), Fig. 2 (c), Fig. 2 (d) are conventional mesh parameter schematic diagram, and rib is calculated by formula (3) Tension and compression rigidity.It is by the off-axis rigidity that rib angle and formula (6) substitution formula (5) obtain rib：

Formula (10) is substituted into formula (3), superposition obtain all ribs layer vertical, horizontal tension and compression rigidity and：

Rib/covering mass ratio the m of grid Stiffened Cylindrical Shells Under External Pressure is calculated by formula (7)_bWith vertical, horizontal equivalent thickness t_dx、t_dy；

4) internal pressure strength of stiffened cylindrical shell is calculated

4.1) axial stress σ of the grid reinforcement post shell under inner pressuring load P effects is calculated according to formula (8)_xShould with ring Power σ_y；

4.2) according to formula T_zh=T- π R²P_F, calculate the equivalent axle compressive load T under axle pressure, inner pressuring load effect_zh；

Work as T_zhWhen≤0, the internal pressure ultimate bearing capacity of stiffened cylindrical shell is：

Work as T_zhDuring ＞ 0, the internal pressure ultimate bearing capacity of stiffened cylindrical shell is：

For example, to the equilateral triangle grid Stiffened Cylindrical Shells Under External Pressure of r=0, substituting into formula (7) by 0 °/± 60 ° and obtaining rib covering matter Amount than andIt is vertical, ring equivalent thickness is respectivelyt_dx=t_dy=t_s(1+0.375m_b)。

T_zhWhen≤0, by t_dx、t_dySubstitute intoObtaining internal pressure ultimate bearing capacity is：

T_zhDuring ＞ 0, by t_dx、t_dySubstitute intoObtaining internal pressure ultimate bearing capacity is：

For verification the verifying results, certain inner pressuring load is carried out to 8 examples in table 1 using the method and finite element method Stress and internal pressure ultimate bearing capacity comparing calculation under effect.

The grid reinforced structure parameter (unit of table 1：Length mm)

Stress contrast under certain load effect is shown in Table 2.Take the covering circumference stress maximum σ of finite element analysis_max, most Small value σ_minAverage value and analytical Calculation circumference stress value σ_yContrast, as a result coincide fine, relative mistake (absolute value) is maximum It is 1.47%, minimum 0.09%.

The covering circumference stress of table 2 is contrasted

Ultimate bearing capacity contrast is shown in Table 3.Finite element analysis reaches material limits intensity with covering ring maximum stress Failure criteria obtains structure internal pressure ultimate bearing capacity, as a result coincide fine, and relative mistake (absolute value) is 3.02%, minimum to the maximum It is 0.36%.

The load-bearing capacity analysis result of table 3

This patent provides a kind of accurate Analytic Calculation Method for the design of complex mesh stiffening shell internal pressure strength, fits For various grid configuration structures, the internal pressure strength design under pure internal pressure and axle pressure, moment of flexure, the effect of internal pressure connected load is calculated, Obtain its ultimate bearing capacity.The method is more more visual and clear than finite element method, succinct convenience, only considers that covering is carried than former The method of effect is more accurate, is conducive to improving grid reinforced structure bearing capacity, mitigates construction weight, realizes the accurate of intensity Quick design.

Claims (1)

1. a kind of computational methods of stiffened cylindrical shell internal pressure strength accurate Analysis, it is characterised in that following steps：

The first step, " paving " treatment is carried out to the rib in stiffened cylindrical shell

By rib by etc. rigidity " paving " treatment, the rib of same angle is equivalent to one layer of equivalent " orthogonal " anisotropic band, net Lattice stiffening part changes into the Orthotropic Laminates being made up of the grid rib layer of different angles；

If it is t that the angle of rib and housing axis is θ, width_w, rib spacing be b_s, material be along the elastic modelling quantity in rib direction E, then the rib of same angle constitute monovalent orthotropy layer；The deflection of equivalent orthotropy layer is rib With the angle theta of housing axis, it is equivalent that elastic constant presses formula (1)：

$\left.\begin{array}{c}{E}_1=E(t_w+t_{wA})/b_s\\ E_2=0\\ v_{12}=0\\ G_{12}=0\end{array}\right\}---\left(1\right)$

Wherein, E₁It is longitudinal modulus of elasticity；E₂It is transverse modulus of elasticity；ν₁₂It is main Poisson's ratio；G₁₂It is longitudinal-transverse shear modulus；Subscript 1st, 2 is material direction；t_wAIt is the equivalent width of rib fillet, is calculated by formula (2)：

$t_{wA}=(2-\mathrm{\π}/2)\frac{r^2}{h}---\left(2\right)$

Wherein, r is rib radius of corner；H be rib highly；

Second step, calculates the tension and compression rigidity of rib

The tension and compression rigidity A of Orthotropic Laminates_ijCalculated by formula (3)：

$A_{ij}=\underset{k=1}{\overset{n}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k-z_{k-1})---\left(3\right)$

Wherein, n is the number of plies；z_k、z_k-1It is the coordinate on the upper and lower surface of kth layer；To be transformed into the rigidity element of structure principal direction, Referred to as off-axis rigidity；

Described off-axis rigidity is converted to by formula (4) by positive axis rigidity：

$\left.\begin{array}{c}\stackrel{-}{Q_{\mathrm{11}}}=Q_{11}{L}^4+2(Q_{12}+2Q_{66})L^2{M}^2+Q_{22}{M}^4\\ \stackrel{-}{Q_{22}}=Q_{11}{M}^4+2(Q_{12}+2Q_{66})L^2{M}^2+Q_{22}{L}^4\\ \stackrel{-}{Q_{12}}=(Q_{11}+Q_{\mathrm{22}}-4Q_{66})L^2{M}^2+Q_{12}(L^4+M^4)\\ \stackrel{-}{Q_{16}}=(Q_{11}-Q_{\mathrm{12}}-2Q_{66})L^{3}M+(Q_{12}-Q_{\mathrm{22}}+2Q_{66}){\mathrm{LM}}^3\\ \stackrel{-}{Q_{26}}=(Q_{11}-Q_{\mathrm{12}}-2Q_{66}){\mathrm{LM}}^3+(Q_{12}-Q_{\mathrm{22}}+2Q_{66})L^{3}M\\ \stackrel{-}{Q_{66}}=(Q_{11}+Q_{\mathrm{22}}-2Q_{\mathrm{12}}-2Q_{66})L^2{M}^2+Q_{66}(L^4+M^4)\\ L=\cos \left({\mathrm{\θ}}_k\right)\\ M=\sin \left({\mathrm{\θ}}_k\right)\end{array}\right\}---\left(4\right)$

Wherein, Q_ijIt is the rigidity element of laminated material principal direction, referred to as positive axis rigidity, its subscript 1 is material principal direction, 2 is material Expect horizontal, 3 directions according to the rotation direction that right-handed coordinate system determination, 6 are around 3 axles；

Described positive axis rigidity is pressed formula (5) and is calculated by elastic properties of materials constant：

$\left.\begin{array}{c}{Q}_{11}=E_1/(1-{v_{12}}^2\frac{E_2}{E_1})\\ Q_{22}=E_2/(1-{v_{12}}^2\frac{E_2}{E_1})\\ Q_{12}=Q_{12}=v_{12}{Q}_{22}\\ Q_{66}=G_{12}\end{array}\right\}---\left(5\right)$

Formula (1) is substituted into formula (5) and obtains every layer of positive axis rigidity of rib equivalent layer, such as shown in formula (6)：

$\left.\begin{array}{c}{Q}_{11}=\frac{E(t_w+t_{wA})}{b_s}\\ Q_{22}=Q_{12}=Q_{66}=0\end{array}\right\}---\left(6\right)$

3rd step, calculates stiffened cylindrical shell vertical, horizontal equivalent thickness

Rib vertical, horizontal tension and compression rigidity A is obtained by formula (3)₁₁、A₂₂, draw grid Stiffened Cylindrical Shells Under External Pressure rib/covering mass ratio m_b, indulge, Horizontal equivalent thickness t_dx、t_dyComputing formula (7)：

$\left.\begin{array}{c}{t}_{dx}=t_s(1+\frac{m_b}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\cos }^4{\mathrm{\θ}}_k)\\ t_{dy}=t_s(1+\frac{m_b}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\sin }^4{\mathrm{\θ}}_k)\\ m_b=\frac{\underset{k=1}{\overset{m}{\mathrm{\Σ}}}\frac{h_k(t_{wk}+t_{wAk})}{b_{sk}}}{t_s}\end{array}\right\}---\left(7\right)$

Wherein, t_sIt is skin thickness；M is the rib angle number for constituting grid；

4th step, calculates the internal pressure strength of stiffened cylindrical shell

4.1) Stress calculation under internal pressure effect

To stiffened cylindrical shell containing end socket, the axial stress σ under inner pressuring load P effects_x, circumference stress σ_yComputing formula point It is not：

$\left.\begin{array}{c}{\mathrm{\σ}}_x=\frac{PR}{2t_{dx}}\\ {\mathrm{\σ}}_y=\frac{PR}{t_{dy}}\end{array}\right\}---\left(8\right)$

In formula, R is stiffened cylindrical shell housing radius；

To the stiffened cylindrical shell without end socket, there is axial stress σ_x=0；

4.2) Strength Failure criterion

To holding interior laminated structure, using the 3rd strength theory, i.e. maximum shear stress failure criteria, such as shown in formula (9)：

σ₁-σ₃≤σ_b (9)

Wherein, σ₁First principal stress is the circumference stress that internal pressure is producedσ₃It is third principal stress；

4.3) axle pressure is calculated with the internal pressure strength under internal pressure synergy

Axle is pressed and is with the equivalent axle compressive load under the effect of end socket internal pressure connected load：T_zh=T- π R²P_F, wherein, T is maximum internal pressure Axle pressure under design conditions, P_FIt is grid reinforcement post shell front head pressure；

Work as T_zhWhen≤0, third principal stress σ₃=0；By σ₁、σ₃The internal pressure limit that substitution formula (9) obtains stiffened cylindrical shell is held Loading capability is：

Work as T_zhDuring ＞ 0, third principal stress is the axial compression stress that axle pressure is producedBy σ₁、σ₃Formula (9) is substituted into obtain The internal pressure ultimate bearing capacity of stiffened cylindrical shell is：The internal pressure of described stiffened cylindrical shell Ultimate bearing capacity is the internal pressure strength of stiffened cylindrical shell.