阅读说明：本技术 一种基于雪载荷作用下柔性体承载重量预测方法及系统 (method and system for predicting bearing weight of flexible body under snow load ) 是由 王单 王健 于 2019-10-28 设计创作，主要内容包括：本发明公开一种基于雪载荷作用下柔性体承载重量预测方法及系统,所述预测方法确定雪载荷在柔性体表面的分布模式；当所述分布模式为三角形堆垛,则根据第一载荷分布公式预测雪载荷作用下柔性体的承载重量；当所述分布模式为梯形堆垛,则根据第二载荷分布公式预测雪载荷作用下柔性体的承载重量,从而实现对雪灾的预防及检测；可见采用本发明中的方法进行预测,无需针对不同的柔性体进行不同实验,因此降低了实验方法的工作量。(The invention discloses flexible body bearing weight prediction methods and systems based on snow load, wherein the prediction method determines a distribution mode of snow load on the surface of a flexible body, when the distribution mode is triangular stacking, the bearing weight of the flexible body under the snow load is predicted according to a th load distribution formula, when the distribution mode is trapezoidal stacking, the bearing weight of the flexible body under the snow load is predicted according to a second load distribution formula, and therefore snow disaster prevention and detection are achieved.)

1, prediction method of flexible body bearing weight based on snow load, characterized in that, the prediction method includes:

determining a distribution mode of the snow load on the surface of the flexible body;

when the distribution mode is triangular stacking, predicting the bearing weight of the flexible body under the action of snow load according to an th load distribution formula;

and when the distribution mode is trapezoidal stacking, predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula.

2. The method of predicting the weight carried by a flexible body under snow load according to claim 1, further comprising:

and determining the structural deformation degree of the flexible body according to the bearing weight of the flexible body.

3. The method for predicting the load bearing weight of the flexible body under the snow load according to claim 2, wherein the structural deformation degree of the flexible body is determined according to the load bearing weight of the flexible body, and the specific formula is as follows:

wherein, W_fThe load weight of the flexible body is rho, the density of the snow load, g, the gravity acceleration, L and α, the maximum friction angle between the snow load and the surface of the flexible body is obtained.

4. The method for predicting the load bearing weight of the flexible body under the snow load according to claim 1, wherein when the distribution mode is a triangular stacking, the method for predicting the load bearing weight of the flexible body under the snow load according to the th load distribution formula specifically comprises:

determining a snow load distribution height function according to a th load distribution formula;

and determining the bearing weight of the flexible body according to the th snow load distribution height function.

5. The method for predicting the bearing weight of the flexible body under the snow load according to claim 1, wherein when the distribution mode is a trapezoidal stacking mode, the method for predicting the bearing weight of the flexible body under the snow load according to a second load distribution formula specifically comprises:

determining a second snow load distribution height function according to a second load distribution formula;

and determining the bearing weight of the flexible body according to the second snow load distribution height function.

6. The method for predicting the load bearing weight of the flexible body under the snow load according to claim 4, wherein the load distribution formula is as follows:

h (t) is th snow load distribution height function, α is the maximum friction angle between the snow load and the surface of a flexible body, theta is the included angle between the normal direction of the beam section at the arc length s after deformation and the normal direction of the section before deformation, t is s/L, s is the arc length, L is the length, the self-weight influence factor M is M/rho L, rho is the density of the snow load, M is the mass, and the Cauchy number CY is rho gL⁴And B, g is gravity acceleration, and B is flexibility.

7. The method for predicting the load bearing weight of the flexible body under the snow load according to claim 5, wherein the second load distribution formula is as follows:

h (u) is a second snow load distribution height function, α is a maximum friction angle between the snow load and the surface of the flexible body, θ is an included angle between a beam section normal direction and a beam section normal direction at a post-deformation arc length s and a pre-deformation section normal direction, t is s/L, s is the arc length, L is the length, a self-weight influence factor M is M/ρ L, ρ is the density of the snow load, M is the mass, and the cauchy number CY is ρ gL⁴G is gravitational acceleration, B is flexibility, h_cIs the critical height.

8, prediction system for the load bearing weight of flexible body under the action of snow load, characterized in that, the prediction system includes:

the distribution mode determining module is used for determining the distribution mode of the snow load on the surface of the flexible body;

a load weight determination module for predicting the load weight of the flexible body under the action of snow load according to load distribution formula when the distribution mode is triangular stacking;

and the second bearing weight determining module is used for predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula when the distribution mode is the trapezoidal stacking.

9. The system for predicting the bearing weight of the flexible body under the snow load according to claim 8, wherein the bearing weight determining module specifically comprises:

an th snow load distribution height function determining unit for determining a th snow load distribution height function according to a th load distribution formula;

, a load weight determination unit for determining the load weight of the flexible body according to the snow load distribution height function.

10. The system for predicting the load bearing capacity of the flexible body under the snow load according to claim 8, wherein the second load bearing capacity determining module specifically comprises:

a second snow load distribution height function determining unit for determining a second snow load distribution height function according to a second load distribution formula;

and the second bearing weight determining unit is used for determining the bearing weight of the flexible body according to the second snow load distribution height function.

Technical Field

The invention relates to the technical field of load bearing capacity testing of flexible structures, in particular to flexible body load bearing weight prediction methods and systems based on snow load.

Background

Willows swaying in wind, algae swinging in water, branches bent by snow and the like are common phenomena in nature, kinds of wisdom are stored in the flexible structures, namely external force load borne is reduced through structural deformation of the flexible structures, and bearing capacity of the flexible structures is improved.

The structural deformation of the flexible body can reduce the resistance, which is of great reference significance in engineering. Most of the structures in the engineering are rigid, the rigid structures do not deform obviously when bearing loads, but the corresponding borne resistance is also larger. Therefore, under certain environments, when the requirement on deformation is not high, a flexible structure can be considered to reduce the bearing resistance. At present, relevant engineering examples are wind driven generators with cone concepts, flexible wings of micro aerocars, flapping wing propulsion, gas transfer through hollow flexible fibers in sludge sewage treatment processes and the like.

In areas with severe snow disasters, branches, houses and the like are often pressed to be deformed greatly, and economic losses caused by snow loads are also very obvious every year. Because of the complexity of components, natural snow is mixed with white frost, ice and the like, and direct research has great limitation. At present, the bearing capacity analysis of the flexible body under the action of wind load and fluid load has related theoretical work, but the bearing capacity analysis of the flexible body under the action of solid load, such as the bearing capacity analysis of branches under the action of snow load, is mainly based on an experimental method for researching the influence of parameters such as density, cohesion and the like of snow on the bearing capacity, namely different experiments are needed for different flexible bodies, and the conclusion of universality is difficult to obtain, so the experimental method has large workload.

Disclosure of Invention

The invention aims to provide methods and systems for predicting the bearing weight of a flexible body under the action of snow load, and predicting the bearing weight and the structural deformation degree of the flexible body under the action of the snow load, so as to realize the prevention and detection of snow disasters.

In order to achieve the purpose, the invention provides methods for predicting the bearing weight of a flexible body under the action of snow load, which comprises the following steps:

determining a distribution mode of the snow load on the surface of the flexible body;

when the distribution mode is triangular stacking, predicting the bearing weight of the flexible body under the action of snow load according to an th load distribution formula;

and when the distribution mode is trapezoidal stacking, predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula.

Optionally, the prediction method further includes:

and determining the structural deformation degree of the flexible body according to the bearing weight of the flexible body.

Optionally, the structural deformation degree of the flexible body is determined according to the bearing weight of the flexible body, and the specific formula is as follows:

wherein, W_fThe load weight of the flexible body is rho, the density of the snow load, g, the gravity acceleration, L and α, the maximum friction angle between the snow load and the surface of the flexible body is obtained.

Optionally, when the distribution mode is a triangular stacking, predicting the load bearing weight of the flexible body under the action of the snow load according to a th load distribution formula, specifically including:

determining a snow load distribution height function according to a th load distribution formula;

and determining the bearing weight of the flexible body according to the th snow load distribution height function.

Optionally, when the distribution mode is a trapezoidal stacking, predicting the load bearing weight of the flexible body under the snow load according to a second load distribution formula specifically includes:

determining a second snow load distribution height function according to a second load distribution formula;

and determining the bearing weight of the flexible body according to the second snow load distribution height function.

Optionally, the th load distribution formula is:

h (t) is th snow load distribution height function, α is the maximum friction angle between the snow load and the surface of the flexible body, theta is the included angle between the normal direction of the beam section at the arc length s after deformation and the normal direction of the section before deformation, t is s/L, s is the arc length, L is the length, the self-weight influence factor M is M/rho L, and rho isDensity of snow load, m is mass, and cauchy number CY ═ ρ gL⁴And B, g is gravity acceleration, and B is flexibility.

Optionally, the second load distribution formula is:

h (u) is a second snow load distribution height function, α is a maximum friction angle between the snow load and the surface of the flexible body, θ is an included angle between a beam section normal direction and a beam section normal direction at a post-deformation arc length s and a pre-deformation section normal direction, t is s/L, s is the arc length, L is the length, a self-weight influence factor M is M/ρ L, ρ is the density of the snow load, M is the mass, and the cauchy number CY is ρ gL⁴G is gravitational acceleration, B is flexibility, h_cIs the critical height.

The invention also provides prediction systems for the bearing weight of the flexible body under the action of snow load, which comprises:

the distribution mode determining module is used for determining the distribution mode of the snow load on the surface of the flexible body;

a load weight determination module for predicting the load weight of the flexible body under the action of snow load according to load distribution formula when the distribution mode is triangular stacking;

and the second bearing weight determining module is used for predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula when the distribution mode is the trapezoidal stacking.

Optionally, the th bearing weight determining module specifically includes:

an th snow load distribution height function determining unit for determining a th snow load distribution height function according to a th load distribution formula;

, a load weight determination unit for determining the load weight of the flexible body according to the snow load distribution height function.

Optionally, the second bearing weight determining module specifically includes:

a second snow load distribution height function determining unit for determining a second snow load distribution height function according to a second load distribution formula;

and the second bearing weight determining unit is used for determining the bearing weight of the flexible body according to the second snow load distribution height function.

According to the specific embodiment provided by the invention, the invention discloses the following technical effects:

the invention discloses flexible body bearing weight prediction methods and systems based on snow load, wherein the prediction method determines a distribution mode of snow load on the surface of a flexible body, when the distribution mode is triangular stacking, the bearing weight of the flexible body under the snow load is predicted according to a th load distribution formula, when the distribution mode is trapezoidal stacking, the bearing weight of the flexible body under the snow load is predicted according to a second load distribution formula, and therefore snow disaster prevention and detection are achieved.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.

FIG. 1 is a flow chart of a method for predicting the bearing weight of a flexible body under the action of snow load according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a triangular stack and a trapezoidal stack in accordance with an embodiment of the present invention;

FIG. 3 is a schematic diagram illustrating the determination of the maximum friction angle according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of a force applied to a flexible body according to an embodiment of the present invention;

FIG. 5 is a block diagram of a system for predicting the load bearing capacity of a flexible body under snow loading in accordance with an embodiment of the present invention;

FIG. 6 is a graph showing the relationship between the load bearing capacity of the triangular stacking underbeam and the Cauchy number and the self-weight factor of the triangular stacking underbeam according to the embodiment of the invention;

FIG. 7 is a graph showing the relationship between the load bearing capacity, Cauchy number and the weight factor of the trapezoidal stacked lower beam according to the embodiment of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only partial embodiments of of the present invention, rather than all embodiments.

The invention aims to provide methods and systems for predicting the bearing weight of a flexible body under the action of snow load, and predicting the bearing weight and the structural deformation degree of the flexible body under the action of the snow load, so as to realize the prevention and detection of snow disasters.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, a more detailed description is provided below in conjunction with the accompanying drawings and the detailed description.

Fig. 1 is a flowchart of a method for predicting the load bearing weight of a flexible body under the action of a snow load according to an embodiment of the present invention, and as shown in fig. 1, the present invention provides methods for predicting the load bearing weight of a flexible body under the action of a snow load, where the method includes:

step S1: determining a distribution mode of the snow load on the surface of the flexible body;

step S2, when the distribution mode is triangular stacking, the load bearing weight of the flexible body under the action of snow load is predicted according to a load distribution formula;

step S3: and when the distribution mode is trapezoidal stacking, predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula.

The prediction method further comprises the following steps:

step S4: determining the structural deformation degree of the flexible body according to the bearing weight of the flexible body, wherein the specific formula is as follows:

wherein, W_fThe load weight of the flexible body is rho, the density of the snow load, g, the gravity acceleration, L and α, the maximum friction angle between the snow load and the surface of the flexible body is obtained.

The individual steps are discussed in detail below:

step S1: determining the distribution pattern of the snow load on the surface of the flexible body, as shown in fig. 2, the distribution pattern of the present invention includes a triangular stack and a trapezoidal stack, wherein (a) in fig. 2 is the triangular stack, (b) in fig. 2 is a curve in which the arc length s in the triangular stack passes through the centroid of the cross section, (c) in fig. 2 is the trapezoidal stack, and (d) in fig. 2 is a curve in which the arc length s in the trapezoidal stack passes through the centroid of the cross section.

Step S2, when the distribution mode is triangular stacking, the load bearing weight of the flexible body under the action of snow load is predicted according to a load distribution formula, and the method specifically comprises the following steps:

step S21, determining a th snow load distribution height function according to a th load distribution formula, which specifically comprises the following steps:

fig. 4 is a schematic view of the stress of the flexible body according to the embodiment of the present invention, as shown in fig. 4, an arc length s is a curve passing through a centroid of a cross section, θ is an angle between a normal direction of the cross section of the beam at the arc length s after deformation and a normal direction of the cross section before deformation, h is a height (thickness) of the cross section of the beam at the arc length s after deformation, and a control equation of the beam is derived by taking triangular stacking as an example, and the specific derivation process is as follows:

establishing a relation between bending moment and corner in the large-deformation beam:

b is the flexibility, theta is the included angle between the normal direction of the beam section at the position of the arc length s after deformation and the normal direction of the beam section before deformation, and s is the arc length;

the differentiation of the bending moment is as follows:

force balance relationship:

in the X direction:

d(F_ssinθ)-d(F_Tcosθ)＝0 (3)

wherein, F_TTo intercept forces tangential to the arc length on the micro-segment, F_sTo intercept forces on the micro-segment along the normal to the arc length, d () is the increment of the force within the intercepted micro-unit.

Y direction:

d(F_scosθ)+d(F_Tsinθ)＝ρghdx+mgdx (4)

wherein h is the height of the beam section,

the geometrical relationship is as follows:

dx＝ds cosθ (5)

is obtained by the following formulas (1) and (2):

F_s＝Bθ” (6)

the following is derived from equation (3):

F_T＝F_stanθ+C＝Bθ”tanθ+C (7)

the boundary condition of the free end of the beam is F_s＝F_TWhen the constant C is 0, obtained by substituting the equation (7), the equation (7) is adjusted to:

F_T＝Bθ”tanθ (8)

substituting the expression (8) into the expression (4), and after simplification, deriving an equilibrium equation of the deformation beam:

the following dimensionless coordinates and dimensionless quantities are defined:

substituting equation (10) into equation (9) determines the th load distribution equation to be:

h (t) is a th snow load distribution height function, theta is an included angle between a beam section normal direction at an arc length s after deformation and a section normal direction before deformation, t is s/L, s is the arc length, L is the length, a self-weight influence factor M is M/rho L, rho is the density of the snow load, M is the mass, and the Cauchy number CY is rho gL⁴G is gravity acceleration, B is flexibility, α is the maximum friction angle of the snow load acting on the surface of the flexible body, as shown in FIG. 3, small particles are used to simulate the snow load, the particles will be stacked on the surface of the substrate due to the action of cohesion, and the maximum angle at which the particles can be stacked is designated as the maximum friction angle.

Finally, a snow load distribution height function H (t) is determined from the load distribution formula.

Step S22, determining the bearing weight of the flexible body according to the snow load distribution height function, wherein the specific formula is as follows:

where t is s/L, s is arc length, ρ is density of snow load, g is gravity acceleration, L is length, and h (t) is th snow load distribution height function.

Step S3: when the distribution mode is trapezoidal stacking, predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula, which specifically comprises the following steps:

step S31, determining a second snow load distribution height function H (u) according to a second load distribution formula, wherein the specific determination process is similar to the determination of the second load distribution formula and is not repeated in , and the second load distribution formula is as follows:

h (u) is a second snow load distribution height function, α is a maximum friction angle of snow load acting on the surface of the flexible body, and theta is a beam section at the arc length s after deformationThe included angle between the normal direction and the normal direction of the section before deformation, t is s/L, s is arc length, L is length, the self-weight influence factor M is M/rho L, rho is density of snow load, M is mass, and the Cauchy number CY is rho gL⁴G is gravitational acceleration, B is flexibility, h_cCritical height, compliance B ═ EI/W, critical height h_cTan α · W/2L, E is the modulus of elasticity, I is the moment of inertia of the beam section, and W is the width.

Modulus of elasticity E-mgx₀/(bh³12) where b is the width of the beam section and h is the height (thickness) of the beam section mgx₀Is the bending moment of the fixed end.

And finally determining a second snow load distribution height function H (u) according to the second load distribution formula.

Step S32: determining the bearing weight of the flexible body according to the second snow load distribution height function, wherein the specific formula is as follows:

where u is 1-t, t is s/L, s is arc length, ρ is density of snow load, g is gravitational acceleration, L is length, and h (u) is a second snow load distribution height function.

Fig. 5 is a structural diagram of a system for predicting the load weight of a flexible body under the action of snow load according to an embodiment of the present invention, and as shown in fig. 5, the present invention further provides systems for predicting the load weight of a flexible body under the action of snow load, where the prediction systems include:

the distribution mode determining module 1 is used for determining the distribution mode of the snow load on the surface of the flexible body;

a load weight determination module 2, for predicting the load weight of the flexible body under the action of snow load according to load distribution formula when the distribution mode is triangular stacking;

and the second bearing weight determining module 3 is used for predicting the bearing weight of the flexible body under the action of the snow load according to a second load distribution formula when the distribution mode is the trapezoidal stacking.

The prediction system further comprises:

the structure deformation degree determining module is used for determining the structure deformation degree of the flexible body according to the bearing weight of the flexible body, and the specific formula is as follows:

wherein, W_fThe load weight of the flexible body is rho, the density of the snow load, g, the gravity acceleration, L and α, the maximum friction angle between the snow load and the surface of the flexible body is obtained.

The th bearing weight determining module 2 specifically comprises:

snow load distribution height function determining unit for determining snow load distribution height function according to load distribution formula, wherein the load distribution formula is:

h (t) is th snow load distribution height function, α is the maximum friction angle between the snow load and the surface of a flexible body, theta is the included angle between the normal direction of the beam section at the arc length s after deformation and the normal direction of the section before deformation, t is s/L, s is the arc length, L is the length, the self-weight influence factor M is M/rho L, rho is the density of the snow load, M is the mass, and the Cauchy number CY is rho gL⁴And B, g is gravity acceleration, and B is flexibility.

, a load weight determination unit for determining the load weight of the flexible body according to the snow load distribution height function, wherein the specific formula is as follows:

where t is s/L, s is arc length, ρ is density of snow load, g is gravity acceleration, L is length, and h (t) is th snow load distribution height function.

The second bearing weight determining module 3 specifically includes:

a second snow load distribution height function determining unit, configured to determine a second snow load distribution height function according to a second load distribution formula, where the second load distribution formula is:

h (u) is a second snow load distribution height function, α is a maximum friction angle between the snow load and the surface of the flexible body, θ is an included angle between a beam section normal direction and a beam section normal direction at a post-deformation arc length s and a pre-deformation section normal direction, t is s/L, s is the arc length, L is the length, a self-weight influence factor M is M/ρ L, ρ is the density of the snow load, M is the mass, and the cauchy number CY is ρ gL⁴G is gravity acceleration, flexibility B is EI/W, critical height h_cTan α · W/2L, E is the modulus of elasticity, I is the moment of inertia of the beam section, and W is the width.

A second load weight determining unit, configured to determine a load weight of the flexible body according to the second snow load distribution height function, where the specific formula is:

where u is 1-t, t is s/L, s is arc length, ρ is density of snow load, g is gravitational acceleration, L is length, and h (u) is a second snow load distribution height function.

Fig. 6 is a graph showing the relationship between the load and the cauchy number and the weight factor of a triangular stacked lower beam according to an embodiment of the present invention, in which fig. 6 (a) shows the relationship between the degree of structural deformation and the cauchy number when α ° and M0.01 are equal to 30 °, (b) shows the deformation of the beam when α ° and M0.01 and CY 0.01 are equal to 0.01 when the beam is substantially rigid, in fig. 6 (c) shows the deformation of the beam when α ° and M0.01 and CY 100 are equal to 30 ° and CY 0.01 when the beam has a constant degree of deformation of , and (d) shows the relationship between the load and the cauchy number and the weight factor when α °, 30 ° and 60 ° and M0.01, respectively, are equal to 0.01 when the triangular stacked lower beam according to an embodiment of the present invention

The curve with CY, and (e) in FIG. 6 shows that when α is equal to 30 DEG, M is equal to 0.1,0.01 and 0.001, respectively

Curve as a function of CY.

Fig. 7 is a graph showing the relationship between the load and the cauchy number and the weight factor of the trapezoidal stacked underbeam according to the embodiment of the present invention, as shown in fig. 7, (a) in fig. 7 shows the relationship between the degree of structural deformation and the cauchy number when α ° is 30 ° and M is 0.01, (b) in fig. 7 shows the deformation of the beam when α ° is 30 ° and M is 0.01 and CY is 0.01 when the beam is substantially rigid, (c) in fig. 7 shows the deformation of the beam when α ° is 30 ° and M is 0.01 and CY is 100 when the beam has a constant degree of deformation of , (d) in fig. 7 shows the deformation of the beam when α °, 30 ° and 60 ° respectively, and M is 0.01 when the beam is α °, 45 ° and 60 ° respectively, and M is 0.01Curve with CY, FIG. 7 (e) shows the values when α is equal to 30 °, M is equal to 0.01,0.05 and 0.001, respectively

Curve as a function of CY.

The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.

The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core idea of the present invention, and to those skilled in the art with variations in the specific embodiments and applications of the invention.