CN109145377B - The plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method of predeformation is considered under a kind of thermal environment - Google Patents

The plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method of predeformation is considered under a kind of thermal environment Download PDF

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CN109145377B
CN109145377B CN201810796734.3A CN201810796734A CN109145377B CN 109145377 B CN109145377 B CN 109145377B CN 201810796734 A CN201810796734 A CN 201810796734A CN 109145377 B CN109145377 B CN 109145377B
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matrix
predeformation
stiffness matrix
thermal environment
linear
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CN109145377A (en
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费庆国
杨轩
李彦斌
吴邵庆
陈强
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Southeast University
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    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention discloses a kind of plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES methods that predeformation is considered under thermal environment, include the following steps: according to the structural material parameter under starting force load and thermal environment, structure linear stiffness matrix, thermal stress stiffness matrix and the nonlinear stiffness matrix for considering predeformation are calculated, linear stiffness matrix, thermal stress stiffness matrix and nonlinear stiffness matrix three are integrated into structure global stiffness matrix；It establishes under thermal environment and considers the plate dynamics equations of predeformation, establish Generalized-grads Theory governing equation according to dynamics equations, then obtain the plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result for considering predeformation under thermal environment by model analysis.Dynamic Characteristics method of the invention has comprehensively considered the influence of geometrical non-linearity caused by predeformation and thermal environment to the rigidity of structure, so as to apply to the VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES under complex load environment, the present invention can effectively improve complex environment lower plate structure Dynamic Characteristics precision, instruct Structural Design.

Description

The plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method of predeformation is considered under a kind of thermal environment
Technical field
The present invention relates to the plates that predeformation is considered under a kind of plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method more particularly to a kind of thermal environment VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method.
Background technique
Hardened structure is widely used in engineering structure, and complicated load environment is faced during military service.Structure is special Property analysis can for structure design provide important guiding.On the one hand, due to preloading, the factors such as dead load and manufacturing process It influences, hardened structure is commonly present predeformation, has on the dynamic characteristic of structure and significantly affects.On the other hand, due to the work of fuel factor With thermal environment lower plate structure Dynamic Characteristics need to consider the influence of the factors such as thermal stress.
Therefore, in order to preferably instruct structure to design and play structural behaviour, it would be highly desirable to develop under a kind of thermal environment consider it is pre- The plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method of deformation.
Summary of the invention
Goal of the invention: the object of the present invention is to provide one kind to effectively improve complex environment lower plate structure Dynamic Characteristics precision Thermal environment under consider predeformation plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method.
Technical solution: in order to achieve the above object, the invention discloses a kind of hardened structure of consideration predeformation under thermal environment is dynamic Characteristic analysis method includes the following steps:
(1), according to the structural material parameter under starting force load and thermal environment, structure linear stiffness matrix is calculated, heat is answered Power stiffness matrix and the nonlinear stiffness matrix for considering predeformation, by linear stiffness matrix, thermal stress stiffness matrix and non-linear Stiffness matrix three is integrated into structure global stiffness matrix；
(2), it establishes under thermal environment and considers the plate dynamics equations of predeformation, established according to dynamics equations wide Adopted Characteristic Problem governing equation, then the plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES knot that predeformation is considered under thermal environment is obtained by model analysis Fruit.
Wherein, in the step (1), the structural material parameter includes the elasticity modulus of different directions, different directions Modulus of shearing, the Poisson's ratio of different directions, thermal expansion coefficient and density of material.
Preferably, the specific steps of structure global stiffness matrix are calculated in the step (1) are as follows:
The corresponding material parameter of structure is determined according to current thermal environment first, establishes structure linear stiffness matrix KL, calculate Formula is as follows:
B in formulaLFor linear geometry matrix, D is structural elasticity matrix, and V is integral domain, BL TFor turning for linear geometry matrix Set matrix；
Then the nonlinear stiffness matrix K for considering structure predeformation is established according to von Karman nonlinear theoryNL, KNL By unit nonlinear stiffness matrix Ke NLSuperposition obtains, Ke NLCalculation formula is as follows:
B is the linear cell geometry matrix of structure, B in formulaNLFor non-linear unit geometric matrix, BNL TIt is several for non-linear unit The transposed matrix of what matrix；
Thermal force T is calculated second by finite element methodloadStructure thermal stress field σ under effectT, and answered according to structure heat Field of force σTCalculate its corresponding thermal stress stiffness matrix Kσ, calculation formula is as follows:
Kσ=∫VGTσTGdV
In formula, G is gradient of the unit shape function in all directions, GTFor unit shape function the gradient of all directions transposition square Battle array；
The structure global stiffness matrix K that predeformation is considered under thermal environment is finally calculated, calculation formula is as follows:
K=KL+KNL+Kσ。
Furthermore the specific steps of VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result are calculated in the step (2) are as follows:
The plate dynamics equations that predeformation is considered under thermal environment are initially set up, calculation formula is as follows:
In formula, M is architecture quality matrix, C is structural damping matrix, x is structure node transposed matrix；
Generalized-grads Theory governing equation is established further according to dynamics equations, calculation formula is as follows:
(K-ω2M) A=0
In formula, ω is structure frequency, A is each node amplitude matrix, obtains finally by model analysis and considers under thermal environment The plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result of predeformation.
Further, in the step (2) VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result include hardened structure modal frequency and structural eigenvector.
The utility model has the advantages that compared with prior art, the present invention has following remarkable advantage: Dynamic Characteristics method of the invention The influence of geometrical non-linearity caused by predeformation and thermal environment to the rigidity of structure is comprehensively considered, so as to apply to complexity VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES under load environment, the present invention can effectively improve complex environment lower plate structure Dynamic Characteristics precision, Instruct Structural Design.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is hardened structure Z-direction predeformation cloud atlas in the present invention；
Fig. 3 is hardened the 1st first order mode cloud atlas of structure in the present invention；
Fig. 4 is hardened the 2nd first order mode cloud atlas of structure in the present invention；
Fig. 5 is hardened the 3rd first order mode cloud atlas of structure in the present invention；
Fig. 6 is hardened the 4th first order mode cloud atlas of structure in the present invention；
Fig. 7 is hardened the 5th first order mode cloud atlas of structure in the present invention；
Fig. 8 is hardened the 6th first order mode cloud atlas of structure in the present invention；
Fig. 9 is hardened the 7th first order mode cloud atlas of structure in the present invention；
Figure 10 is hardened the 8th first order mode cloud atlas of structure in the present invention；
Figure 11 is hardened the 9th first order mode cloud atlas of structure in the present invention；
Figure 12 is hardened the 10th first order mode cloud atlas of structure in the present invention.
Specific embodiment
Technical solution of the present invention is described further with reference to the accompanying drawing.
As shown in Figure 1, the present invention provides a kind of plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method that predeformation is considered under thermal environment, including Following steps:
(1), according to the structural material parameter under starting force load and thermal environment, structure linear stiffness matrix is calculated, heat is answered Power stiffness matrix and the nonlinear stiffness matrix for considering predeformation, by linear stiffness matrix, thermal stress stiffness matrix and non-linear Stiffness matrix three is integrated into structure global stiffness matrix；Calculate the specific steps of structure global stiffness matrix are as follows:
The corresponding material parameter of structure is determined according to current thermal environment first, establishes structure linear stiffness matrix KL, calculate Formula is as follows:
B in formulaLFor linear geometry matrix, D is structural elasticity matrix, and V is integral domain, BL TFor turning for linear geometry matrix Set matrix；
Then the nonlinear stiffness matrix K for considering structure predeformation is established according to von Karman nonlinear theoryNL, KNL By unit nonlinear stiffness matrix Ke NLSuperposition obtains, Ke NLCalculation formula is as follows:
B is the linear cell geometry matrix of structure, B in formulaNLFor non-linear unit geometric matrix, BNL TIt is several for non-linear unit The transposed matrix of what matrix；
Thermal force T is calculated second by finite element methodloadStructure thermal stress field σ under effectT, and answered according to structure heat Field of force σTCalculate its corresponding thermal stress stiffness matrix Kσ, calculation formula is as follows:
Kσ=∫VGTσTGdV
In formula, G is gradient of the unit shape function in all directions, GTFor unit shape function the gradient of all directions transposition square Battle array；
The structure global stiffness matrix K that predeformation is considered under thermal environment is finally calculated, calculation formula is as follows:
K=KL+KNL+Kσ
By taking plate as an example, geometric dimension is chosen for 280mm × 380mm × 2mm, and structural material parameter is as shown in table 1, table Middle E1And E2Respectively 1 and 2 direction elasticity modulus, G12、G13And G23The direction of respectively 12,13 and 23 modulus of shearing, μ12And μ21Point Not Wei 12 and 21 direction Poisson's ratios, a is thermal expansion coefficient, and ρ is density of material.Plate initial displacement field is as shown in Fig. 2, thermal force For homogeneous temperature field Tload=30 DEG C, hardened structure surrounding freely-supported.
1 material properties of table
(2) establishes under thermal environment the plate dynamics equations for considering predeformation, and calculation formula is as follows:
In formula, M is architecture quality matrix, C is structural damping matrix, x is structure node transposed matrix；
Generalized-grads Theory governing equation is established according to dynamics equations, calculation formula is as follows:
(K-ω2M) A=0
In formula, ω is structure frequency, A is each node amplitude matrix, then is obtained by model analysis and considered in advance under thermal environment The modal frequency and structural eigenvector of the hardened structure of deformation, i.e. VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result.
Preceding 10 rank modal frequency of the invention is as shown in table 2, and the preceding 10 stage structure vibration shape is as shown in Fig. 3-Figure 12.
10 rank modal frequency before table 2
Dynamic Characteristics method of the invention has comprehensively considered geometrical non-linearity caused by predeformation and thermal environment to structure The influence of rigidity, so as to apply to the VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES under complex load environment, the present invention can be effectively improved Complex environment lower plate structure Dynamic Characteristics precision, instructs Structural Design.
Embodiments of the present invention are described in detail in conjunction with attached drawing above, but the present invention is not limited to described reality Apply mode.For those of ordinary skill in the art, in the range of the principle of the present invention and technical idea, to these implementations Mode carries out a variety of variations, modification, replacement and deformation and still falls in protection scope of the present invention.

Claims (1)

1. considering the plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES method of predeformation under a kind of thermal environment, which comprises the steps of:
(1), according to the structural material parameter under starting force load and thermal environment, it is rigid that structure linear stiffness matrix, thermal stress are calculated It spends matrix and considers the nonlinear stiffness matrix of predeformation, by linear stiffness matrix, thermal stress stiffness matrix and non-linear rigidity Matrix three is integrated into structure global stiffness matrix, and structural material parameter includes that the elasticity modulus of different directions, different directions are cut Shear modulu, the Poisson's ratio of different directions, thermal expansion coefficient and density of material；Wherein calculate the specific steps of structure global stiffness matrix Are as follows:
The corresponding material parameter of structure is determined according to current thermal environment first, establishes structure linear stiffness matrix KL, calculation formula is such as Shown in lower:
B in formulaLFor linear geometry matrix, D is structural elasticity matrix, and V is integral domain, BL TFor the transposition square of linear geometry matrix Battle array；
Then the nonlinear stiffness matrix K for considering structure predeformation is established according to von Karman nonlinear theoryNL, KNLBy unit Nonlinear stiffness matrix Ke NLSuperposition obtains, Ke NLCalculation formula is as follows:
B is the linear cell geometry matrix of structure, B in formulaNLFor non-linear unit geometric matrix, BNL TFor non-linear unit geometric moment The transposed matrix of battle array；
Thermal force T is calculated second by finite element methodloadStructure thermal stress field σ under effectT, and according to structure thermal stress field σTCalculate its corresponding thermal stress stiffness matrix Kσ, calculation formula is as follows:
In formula, G is gradient of the unit shape function in all directions, GTFor unit shape function the gradient of all directions transposed matrix；
The structure global stiffness matrix K that predeformation is considered under thermal environment is finally calculated, calculation formula is as follows:
K=KL+KNL+Kσ；
(2), it establishes under thermal environment and considers the plate dynamics equations of predeformation, establish broad sense spy according to dynamics equations Sign problem governing equation, then by model analysis obtain under thermal environment consider predeformation plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES as a result, its The middle specific steps for calculating VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result are as follows:
The plate dynamics equations that predeformation is considered under thermal environment are initially set up, calculation formula is as follows:
In formula, M is architecture quality matrix, C is structural damping matrix, x is structure node transposed matrix；
Generalized-grads Theory governing equation is established further according to dynamics equations, calculation formula is as follows:
(K-ω2M) A=0
In formula, ω is structure frequency, A is each node amplitude matrix, obtains finally by model analysis and considers pre- become under thermal environment The plate VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES of shape is as a result, VIBRATION CHARACTERISTIC ANALYSIS OF STRUCTURES result includes the modal frequency and structural eigenvector of hardened structure.
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CN101706833A (en) * 2009-11-25 2010-05-12 哈尔滨工业大学 Design method for marine propeller made of carbon fiber composite material
CN101706832A (en) * 2009-11-25 2010-05-12 哈尔滨工业大学 Optimization design method of fibre enhanced composite material marine propeller blade
CN108287970A (en) * 2018-01-31 2018-07-17 东南大学 Sensitivity Analysis Method of the hot-die state based on two-dimensional quadrature anisotropic composite material plate to structural parameters

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101706833A (en) * 2009-11-25 2010-05-12 哈尔滨工业大学 Design method for marine propeller made of carbon fiber composite material
CN101706832A (en) * 2009-11-25 2010-05-12 哈尔滨工业大学 Optimization design method of fibre enhanced composite material marine propeller blade
CN108287970A (en) * 2018-01-31 2018-07-17 东南大学 Sensitivity Analysis Method of the hot-die state based on two-dimensional quadrature anisotropic composite material plate to structural parameters

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