CN106599506A - Method for confirming support stiffness of cantilever beam to longitudinal deck stringer - Google Patents
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Abstract
The invention provides a method for confirming support stiffness of an elastically fixed cantilever beam to a longitudinal deck stringer and belongs to the technical field of ship structure engineering. The method for confirming the support stiffness of the elastically fixed cantilever beam to the longitudinal deck stringer mainly comprises the following steps: 1) establishing a calculating model for the support stiffness of the cantilever beam to the longitudinal deck stringer; 2) establishing a kinetic equation of the elastically fixed cantilever beam, and acquiring the lowest order frequency formula; 3) establishing a calculating model for the torsion rigidity of an elastically fixed end of the cantilever beam; 4) confirming the torsion rigidity of the elastically fixed end of the cantilever beam; 5) confirming the support stiffness of the cantilever beam to the longitudinal deck stringer; and 6) confirming the key point of ship structure design according to the influence factors for the support stiffness of the cantilever beam to the longitudinal deck stringer. The invention provides the method for confirming the support stiffness of the cantilever beam to the longitudinal deck stringer on an extensively damaged part and establishes a basis for researching the rigidity, strength and stability problems of the damaged ship structure.
Description
Technical field
The present invention relates to the technical field of Ship Structure engineering, is specifically related to hull damage latter resiliently mounted outstanding
Determination method of the arm crossbeam to deck longitudinal support stiffness.
Background technology
Accurate calculating and reasonable assessment to hull residual intensity can be effectively ensured the reasonability and peace of ship structure design
Quan Xing, it is the key for determining deck longitudinal axial bearing capacity that damaged ship hulls component is checked to the support stiffness of deck longitudinal.
Alliance of Association International Des Registres (International Association of Classification Societies,
Abbreviation IACS), the content that the residual intensity after hull beam breakage is checked is increased in the HCSR specifications implemented in 2016.HCSR
The depth and height of the damaged scope of the collision of bulk freighter and oil carrier remaining Ultimate Strength Calculation are defined, but does not specify cut
Length, is typically defaulted as the spacing for being a main support component.But this differs greatly with actual damage length, Norway's ship
The research of level society (DNV) shows that the cut length of impact failure is likely to be breached 0.1L (L is hull overall length), such as by this than arranging based on
Calculate, cut will be across about 3~10 transverse frames, and in so big cut region, the support of deck cross member topside one end is firm
Degree will weaken significantly, cause crossbeam to meet minimum rigidity requirement, will appear from the danger of deck overall collapse.
At present, the calculating to damaged ship hulls structural-load-carrying capacity mainly adopts nonlinear finite element method.Due to non-thread
Property requirement of the FInite Element to computer, software operator it is higher, and substantial amounts of modeling and calculating time need to be spent, to hull
Structure design and Performance Evaluation cause inconvenience, are badly in need of a kind of quick, reasonable and safe determination cantilever support grillage on a large scale
Ultimate bearing capacity theoretical method, and the key of this method is that and finds a kind of resiliently mounted cantilever beams to deck
The determination method of vertical bone support stiffness.
The content of the invention
For problem present in strength and stability calculating after hull beam breakage, after now aiming to provide a kind of hull damage
Determination method of the cantilever beams to deck longitudinal support stiffness, the flow process of this method is:By the deck cross member in damaged scope
One end flexible fastening, the free cantilever beam in one end are regarded as, deck longitudinal is considered as and is supported on resiliently mounted cantilever in damaged scope
On crossbeam, the mechanical model for determining collision rift deck longitudinal support stiffness on a large scale is thus set up;It is resiliently mounted by setting up
The kinetics equation of cantilever beams, solve obtain its minimum order frequency, and carry out series expansion and simplification obtain lowest-order frequency
The computing formula of rate;Fixed end structure is reduced to again the equivalent thin walled beam of two fixed ends, the torsional rigidity of cantilever end is set up
Computation model, and the corresponding relation of the torsion angle according to thin-walled bar torsional restraint problem and complicated bend amount of deflection, it is determined that elastic
The torsional rigidity of fixing end;Finally using stability problem and the similitude of crossbeam Free Vibration Equations, determine resiliently mounted
Support stiffness of the cantilever beams to deck longitudinal;This method can determine that the impact of the vertical bone support stiffness of damaged grillage on a large scale
Factor, obtains quickly and reasonably support stiffness of the cantilever beams to deck longitudinal on a large scale, it is ensured that the conjunction of ship structure design
Rationality.
Concrete technical scheme is as follows:
A kind of determination method of cantilever beams to deck longitudinal support stiffness, including following step:
The first step, sets up computation model of the cantilever beams to deck longitudinal support stiffness;
For the breakage structure of topside on a large scale, the deck cross member in damaged scope is reduced to into one end flexible fastening, one end
Free cantilever beam, and as the support of the deck longitudinal in damaged scope, thus set up collision rift cantilever beams pair on a large scale
The mechanical model that deck longitudinal support stiffness is calculated;
Second step, sets up the kinetics equation of resiliently mounted cantilever beams, obtains its lowest-order frequency formula;
The kinetics equation of resiliently mounted cantilever beams is set up, elastic cantilever crossbeam is obtained most by solving the equation
Low order frequency, and series expansion and simplification are carried out, obtain the computing formula of its minimum order frequency;
3rd step, sets up the torsional rigidity computation model of cantilever beams Elastic Fixed Ends;
The root structure of cantilever beams is generally ship side structure or stringers, is reduced to the equivalent thin of two fixed ends
Wall beam, the computation model of the torsional rigidity of cantilever beams root is set up according to the characteristic of thin walled beam;
4th step, determines the torsional rigidity of the Elastic Fixed Ends of cantilever beams;
According to the torsion angle and the corresponding relation of complicated bend amount of deflection of thin-walled bar torsional restraint problem, cantilever beams are solved
The torsional rigidity of Elastic Fixed Ends;
5th step, determines support stiffness of the cantilever beams to deck longitudinal;
According to stability problem and the similitude of crossbeam Free Vibration Equations, and it is minimum to combine the cantilever beams for determining before this
The computing formula of order frequency, the minimum order frequency of cantilever beams is substituted in corresponding computing formula, obtains resiliently mounted outstanding
Support stiffness of the arm crossbeam to deck longitudinal;
6th step, with reference to analysis of Influential Factors of the cantilever beams to deck longitudinal support stiffness, determines ship structure design
Emphasis.
The good effect of above-mentioned technical proposal is:1st, after obtaining hull breakage on a large scale, deck longitudinal support stiffness
Computing formula, can easily and quickly calculate deck longitudinal support stiffness, be the rigidity of Ship Structure, intensity, stability after breakage
Theory analysis lay the foundation;2nd, by the check to cantilever beams support stiffness, the quality of ship structure design can be instructed
And arrangement, it is cost-effective;3rd, by the analysis of Influential Factors of cantilever beams support stiffness, scientific design Ship Structure,
The security of ship is also greatly improved while improving operating efficiency.
Description of the drawings
Fig. 1 is a kind of flow chart of cantilever beams of the invention to the determination method of deck longitudinal support stiffness;
Fig. 2 is the real figure of deck multispan unstability (20 times) caused by impact failure on a large scale of the invention;
Fig. 3 is the computation model of the deck longitudinal multispan unstability that the cantilever beams of the present invention are supported;
Fig. 4 is the computation model of the torsional rigidity of the cantilever beams Elastic Fixed Ends of the present invention.
Specific embodiment
In order that technological means, creation characteristic, reached purpose and effect that the present invention is realized are easy to understand, it is real below
Apply example and combine accompanying drawing 1 and be specifically addressed to the technical schemes that 4 pairs, the accompanying drawing present invention is provided, but herein below is not as the present invention's
Limit.
The present invention is a kind of determination method of cantilever beams to deck longitudinal support stiffness, and Fig. 1 is that one kind of the present invention is hanged
Arm supports grillage to indulging the flow chart of the determination method of bone support stiffness;As shown in figure 1, the cantilever beams pair that the present embodiment is provided
The determination method of deck longitudinal support stiffness includes following step:
The first step, sets up cantilever beams to indulging the computation model of bone support stiffness;
When ship occurs collision rift on a large scale, the support of the topside grillage of ship to deck disappears, the deformation of ship crossbeam
By the deformation of the crossbeam supported much larger than two ends under good working condition, and the deformation quantity of damaged scope more cross bearer is bigger, such as Fig. 2 institutes
Show.According to the loading characteristic of grillage, there is collision rift on a large scale in ship, support of the topside grillage to deck disappears, now first
Plate can be reduced to the support of three sides, on one side free grillage;And after ship collides breakage, the deck in damaged scope is horizontal
Beam can be reduced to one end flexible fastening, the freely hanging cantilever beam of the other end, and the deck longitudinal in damaged scope is regarded as
It is supported on the crossbeam of cantilever, thus sets up big in colliding rear cross beam on a large scale to the computation model of deck longitudinal support stiffness
The computation model of the vertical bone beam column unstability of scope collision rift grillage, as shown in Figure 3.
Second step, sets up the kinetics equation of resiliently mounted cantilever beams, obtains its lowest-order frequency formula;
In view of the similitude of stability problem and crossbeam Free Vibration Equations, the collision back plate on a large scale with reference to shown in Fig. 3
The computation model of the vertical bone beam column unstability of frame, lists undamped, the motion of small size free vibration of resiliently mounted cantilever beams
Equation:
In above formula, I is cantilever beams cross sectional moment of inertia, and E is the elastic modelling quantity of material, and B is crossbeam span, and M is between vertical bone
Crossbeam quality.
With the separation of variable, if the general solution form of (1) formula is:
V (x, t)=φ (x) Y (t) (2)
For one end flexible fastening, for the cantilever beam that the other end is freely arranged, the perimeter strip that now cantilever beam should meet
Part is:
φ (0)=0 M (0)=k φ ' (0)=EI φ " (0)
M (B)=EI φ " V of (0)=0 (B)=EI φ " (0)=0 (3)
In above formula, B is crossbeam span.
After (1) formula general solution of setting is substituted in the boundary condition (3) that cantilever beam should meet, characteristic equation is obtained such as
Under:
In above formula,Vector is characterized, k is stiffness coefficient, and a is defined as:
In above formula, I is cantilever beams cross sectional moment of inertia, and E is the elastic modelling quantity of material, and M is the crossbeam quality between vertical bone.
The determinant for making (4) formula is zero, and convolution (5), and the frequency equation for thus obtaining cantilever beams is:
In 1+cosh x cos x=cx (cosh x sin x-sinh x cos x) (6) above formula,
X=aB (8)
Power series expansion is carried out to the both sides of frequency equation (6), and casts out high-order in a small amount, solve cantilever beams lowest-order
The formula of frequency:
3rd step, sets up the torsional rigidity computation model of cantilever beams Elastic Fixed Ends;
In Ship Structure, general crossbeam is supported on side wall or stringers, and fixed end structure is reduced to into two fixed ends
Equivalent thin walled beam, and the computation model of the torsional rigidity of cantilever beams Elastic Fixed Ends is set up according to the characteristic of thin walled beam, such as
Shown in Fig. 4.
4th step, determines the torsional rigidity of the Elastic Fixed Ends of cantilever beams;
According to the computation model of the torsional rigidity of the cantilever beams Elastic Fixed Ends set up, and reverse about according to thin-walled bar
The torsion angle of Shu Wenti and the corresponding relation of complicated bend amount of deflection, determine the torsional rigidity of cantilever beams Elastic Fixed Ends.When outstanding
When arm beam is rigidly fixed, now stiffness coefficient k takes large values, and c ≈ 0;During cantilever beam flexible fastening, can be tied according to actual support
The torsional rigidity of structure determines the torsional rigidity of cantilever beam fixing end.
Torsional rigidity is made up of FREE TORSION rigidity and constraint torsional rigidity two parts, due to by the fixing end of cantilever beams
Structure is reduced to the equivalent thin walled beam of two fixed ends, with reference to Structural Mechanics of Thin-Wall, and according to similitude, thin-walled bar is reversed about
The torsion angle of Shu Wenti is corresponding with the amount of deflection of complicated bend problem, and the torsion of cantilever beams Elastic Fixed Ends shown in Fig. 4 is obtained
Turning rigidity is:
In above formula, IωFor stringers or the fan-shaped torsional moment inertia of vertical structure, L is the span (of stringers or vertical structure
As take cut length), E is elastic modelling quantity.
5th step, determines support stiffness of the cantilever beams to deck longitudinal;
According to stability problem and the similitude of crossbeam Free Vibration Equations, and combine the cantilever beams for determining before this most
The formula of low order frequency, the minimum order frequency of cantilever beams is substituted in corresponding calculating analysis mode, obtains resiliently mounted outstanding
Arm crossbeam is to deck longitudinal support stiffness.
The support stiffness of cantilever beams of elastic support as vertical bone is set as K, using stability problem and crossbeam oneself
By the similitude of vibration equation, take beam structure quality and the minimum order frequency of crossbeam square product be resiliently mounted outstanding
Arm crossbeam is to deck longitudinal support stiffness, such as following formula:
K=M ω1 2 (11)
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams.
Formula (5) is substituted in formula (11), obtain resiliently mounted cantilever beams is to deck longitudinal support stiffness:
K=M ω1 2=a4EIb (12)
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams, I is crossbeam
Cross sectional moment of inertia, E is the elastic modelling quantity of material.
Formula (8) is substituted in formula (12), obtain resiliently mounted cantilever beams is to deck longitudinal support stiffness:
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams, I is crossbeam
Cross sectional moment of inertia, E is the elastic modelling quantity of material, and B is crossbeam span.
Formula (9) is substituted in formula (13), obtain resiliently mounted cantilever beams is to deck longitudinal support stiffness:
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams, I is crossbeam
Cross sectional moment of inertia, E is the elastic modelling quantity of material, and B is crossbeam span, and c is cantilever beam cantilever end torsional rigidity.
6th step, with reference to analysis of Influential Factors of the cantilever beams to deck longitudinal support stiffness, determines ship structure design
Emphasis;
Using above formula, analysis of Influential Factors of the cantilever beams to deck longitudinal support stiffness can be carried out, obtain it is quick,
The theoretical method for rationally determining with the deck longitudinal support stiffness damaged on a large scale of safety, and damage length, crossbeam can be learned
End construction and size, vertical bone cross-sectional sizes, spacing of longitudinals, section of beam size, crossbeam spacing, crossbeam span (i.e. grillage width
Degree) and thickness of slab on deck longitudinal support stiffness affect, specify the emphasis of ship structure design, instruct ship structure design, drop
Low cost, raising security.
The present invention preferably mode is these are only, embodiments of the present invention and protection domain is not thereby limited, for
For those skilled in the art, all utilization description of the invention and the equivalent done by diagramatic content should be can appreciate that
Scheme with obtained by obvious change, should be included in protection scope of the present invention.
Claims (5)
1. a kind of determination method of cantilever beams to deck longitudinal support stiffness, including following step:
The first step, sets up computation model of the cantilever beams to deck longitudinal support stiffness;
For the breakage structure of topside on a large scale, the deck cross member in damaged scope is reduced to into one end flexible fastening, one end freedom
Cantilever beam, and as the support of the deck longitudinal in damaged scope, thus set up on a large scale collision rift cantilever beams to deck
The mechanical model that vertical bone support stiffness is calculated;
Second step, sets up the kinetics equation of resiliently mounted cantilever beams, obtains its lowest-order frequency formula;
The kinetics equation of resiliently mounted cantilever beams is set up, the lowest-order of elastic cantilever crossbeam is obtained by solving the equation
Frequency, and series expansion and simplification are carried out, obtain the computing formula of its minimum order frequency;
3rd step, sets up the torsional rigidity computation model of cantilever beams Elastic Fixed Ends;
The root structure of cantilever beams is generally ship side structure or stringers, is reduced to the equivalent thin-walled of two fixed ends
Beam, the computation model of the torsional rigidity of cantilever beams root is set up according to the characteristic of thin walled beam;
4th step, determines the torsional rigidity of the Elastic Fixed Ends of cantilever beams;
According to the torsion angle and the corresponding relation of complicated bend amount of deflection of thin-walled bar torsional restraint problem, cantilever beams elasticity is solved
The torsional rigidity of fixing end;
5th step, determines support stiffness of the cantilever beams to deck longitudinal;
According to stability problem and the similitude of crossbeam Free Vibration Equations, and combine the cantilever beams lowest-order frequency for determining before this
The computing formula of rate, the minimum order frequency of cantilever beams is substituted in corresponding computing formula, obtains resiliently mounted cantilever horizontal
Support stiffness of the beam to deck longitudinal;
6th step, with reference to analysis of Influential Factors of the cantilever beams to deck longitudinal support stiffness, determines the weight of ship structure design
Point.
2. determination method of a kind of cantilever beams according to claim 1 to deck longitudinal support stiffness, wherein, it is described most
Low order frequency and lowest-order frequency formula can be prepared by the following:
(1) when ship occurs collision rift on a large scale, the support of the topside grillage of ship to deck disappears, and the deformation of ship crossbeam will
The deformation of the crossbeam supported much larger than two ends under good working condition;According to the loading characteristic of grillage, occur to collide on a large scale in ship
Afterwards, support of the topside grillage to deck disappears, and deck grillage now can be reduced to the support of three sides, on one side free grillage;It is broken
Deck cross member in the range of damage can simplify one end flexible fastening, the freely hanging cantilever beam of the other end;Deck in damaged scope
On the crossbeam that vertical bone is regarded as being supported on cantilever, thus set up and collide on a large scale meter of the rear cross beam to deck longitudinal support stiffness
Calculate model;
(2) according to the support stiffness computation model of the vertical bone of the grillage of collision rift on a large scale set up, the bullet with crossbeam quality is listed
Property the kinetics equation of cantilever beams fixed, obtain minimum order frequency by solving its characteristic equation, then carry out series expansion
With the formula for simplifying its minimum order frequency of acquisition;
The computation model of the vertical bone beam column unstability of collision rift grillage, and integrated structure dynamics on a large scale, lists undamped, slightly
The equation of motion of the free vibration of the uniform beam of vibration:
In above formula, I is cantilever beams cross sectional moment of inertia, and E is the elastic modelling quantity of material, and B is crossbeam span, and M is the horizontal stroke between vertical bone
Beam quality;
With the separation of variable, if the general solution form of (1) formula is:
V (x, t)=φ (x) Y (t) (2)
For one end flexible fastening, for the free cantilever beam of the other end, the boundary condition that now cantilever beam should meet is:
φ (0)=0 M (0)=k φ ' (0)=EI φ " (0)
M (B)=EI φ " V of (0)=0 (B)=EI φ " (0)=0 (3)
In above formula, B is crossbeam span;
After (1) formula general solution of setting is substituted in the boundary condition (3) that cantilever beam should meet, characteristic equation is obtained as follows:
In above formula,Vector is characterized, k is stiffness coefficient, and a is defined as:
In above formula, I is cantilever beams cross sectional moment of inertia, and E is the elastic modelling quantity of material, and M is the crossbeam quality between vertical bone;
The determinant for making (4) formula is zero, and convolution (5), and the frequency equation for thus obtaining cantilever beams is:
1+cosh x cos x=cx (cosh x sin x-sinh x cos x) (6)
In above formula,
X=aB (8)
Power series expansion is carried out to the both sides of frequency equation (6), and casts out high-order in a small amount, solve the minimum order frequency of cantilever beams
Formula:
。
3. determination method of a kind of cantilever beams according to claim 1 to deck longitudinal support stiffness, wherein, the torsion
Turn rigidity to be calculated as:
In above formula, IωFor stringers or the fan-shaped torsional moment inertia of vertical structure, L is that the span of stringers or vertical structure beam is (general
Take cut length), E is elastic modelling quantity.
4. determination method of a kind of cantilever beams according to claim 2 to deck longitudinal support stiffness, wherein, described
Support rigidity is calculated as:
K=M ω1 2 (11)
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams;
Formula (5) is substituted in formula (11), obtain resiliently mounted cantilever beams is to deck longitudinal support stiffness:
K=M ω1 2=a4EIb (12)
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams, I is used for section of beam
Property square, E for material elastic modelling quantity;
Formula (8) is substituted in formula (12), obtain resiliently mounted cantilever beams is to deck longitudinal support stiffness:
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams, I is used for section of beam
Property square, E for material elastic modelling quantity, B be crossbeam span;
Formula (9) is substituted in formula (13), obtain resiliently mounted cantilever beams is to deck longitudinal support stiffness:
In above formula, M is to indulge the crossbeam quality between bone, ω1For the low-limit frequency of resiliently mounted cantilever beams, I is used for section of beam
Property square, E for material elastic modelling quantity, B be crossbeam span, c be cantilever beam cantilever end torsional rigidity.
5. determination method of a kind of cantilever beams according to claim 1 to deck longitudinal support stiffness, it is determined that on a large scale
Support stiffness influence factor of the damaged cantilever beams to deck longitudinal:
According in above step, analysis of Influential Factors of the cantilever beams to deck longitudinal support stiffness can be carried out, determine crossbeam end
Portion's structure and size, damage length, vertical bone cross-sectional sizes, spacing of longitudinals, section of beam size, crossbeam spacing, crossbeam span are (i.e.
Grillage width), and the size that thickness of slab affects on deck longitudinal support stiffness, carry out the optimization design of Ship Structure.
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CN111553019A (en) * | 2020-04-20 | 2020-08-18 | 哈尔滨工程大学 | Method for calculating residual speed and corner of plate frame crossbeam of revolving body impacting ship body |
CN112784359A (en) * | 2021-01-18 | 2021-05-11 | 浙江工业大学 | Iterative calculation method for constrained torsion limit bearing capacity of thin-wall beam |
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CN109508470A (en) * | 2017-09-22 | 2019-03-22 | 广东工业大学 | The method for establishing ship weight computation model based on deep neural network study |
CN109508470B (en) * | 2017-09-22 | 2022-06-14 | 广东工业大学 | Method for establishing ship weight calculation model based on deep neural network learning |
CN111339614A (en) * | 2020-02-26 | 2020-06-26 | 成都飞机工业(集团)有限责任公司 | Suspension structure rigidity estimation method |
CN111339614B (en) * | 2020-02-26 | 2022-08-12 | 成都飞机工业(集团)有限责任公司 | Suspension structure rigidity estimation method |
CN111553019A (en) * | 2020-04-20 | 2020-08-18 | 哈尔滨工程大学 | Method for calculating residual speed and corner of plate frame crossbeam of revolving body impacting ship body |
CN112784359A (en) * | 2021-01-18 | 2021-05-11 | 浙江工业大学 | Iterative calculation method for constrained torsion limit bearing capacity of thin-wall beam |
CN112784359B (en) * | 2021-01-18 | 2024-04-16 | 浙江工业大学 | Iterative calculation method for constraint torsion limit bearing capacity of thin-wall beam |
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