A stress calculation method for a polycarbonate u-shaped lock hollow plate

Abstract

The application discloses a stress calculation method of a polycarbonate U-shaped lock hollow plate, which comprises the following steps: measuring and determining basic parameters of the U-shaped hollow plate; determining stress equivalent thickness t of the plate σeq ; determining a stress adjustment coefficient η; and calculating and determining the stress σ of the U-shaped hollow plate according to a stress calculation formula. The application provides the stress calculation formula of the polycarbonate U-shaped hollow plate and the determination of related parameters in the formula, and first distinguishes two stress adjustment coefficients η σt and η σp , obtains the tensile stress calculation formula and the compressive stress calculation formula of the U-shaped hollow plate under the condition of large deformation, forms a complete stress calculation system, and fills the blank of the stress calculation theory of the U-shaped hollow plate.

Description

Technical Field

[0001] This invention belongs to the field of stress calculation for polycarbonate hollow boards, and in particular, a method for stress calculation of polycarbonate U-shaped interlocking hollow boards. Background Technology

[0002] Polycarbonate materials are widely used in roofing systems of large public buildings due to their lightweight, high light transmittance, and high impact resistance. Among them, U-shaped interlocking hollow panels are the preferred material for large-span roofs because of their multi-layered cavity structure, excellent waterproof performance, and convenient mechanical connections. However, polycarbonate has a low modulus of elasticity, only 1 / 30 that of glass, which makes U-shaped hollow panels prone to significant deformation under load. Therefore, stress calculations on the panel surface generally need to consider large displacement effects.

[0003] Although existing technologies have proposed improved solutions for displacement calculation, such as the calculation method based on equivalent thickness and displacement reduction factor in patent CN 119004753A, there are still serious deficiencies in the theoretical system for stress calculation, specifically manifested in the following problems:

[0004] I. Limitations of existing stress calculation methods:

[0005] Traditional formula for calculating stress in thin plates ①:

[0006]

[0007] In the formula: σ is the plate surface stress under small displacement, m is the stress coefficient, q is the uniformly distributed load on the plate surface, a is the characteristic width of the plate, and t is the plate thickness. Formula ① is based on the small displacement theory, assuming that the plate is only subjected to bending stress and neglecting the in-plane membrane stress. Its applicable range is mainly ω < t, where ω is the maximum displacement of the plate and t is the plate thickness, i.e., the plate height. However, for U-shaped hollow plates under large deformation ω > t, the membrane stress significantly affects the stress distribution on the plate surface. If the traditional formula is used directly for calculation, Formula ① will produce significant errors, that is, the calculated displacement is larger than the actual displacement, and as the ratio of displacement to plate thickness ω / t increases, the calculated stress becomes unacceptably large, losing its calculation and engineering significance.

[0008] Currently, there is no publicly available formula for calculating the stress of U-shaped hollow slabs. In actual engineering, the specifications, models, and thickness of the U-shaped hollow slabs are mainly matched according to engineering experience based on the span. However, in special circumstances, such as snow loads or wind loads exceeding conventional empirical values, engineering experience becomes unreliable and unsafe.

[0009] II. Problems with existing displacement calculation formulas:

[0010] Although existing technologies introduce an equivalent thickness t eqThe displacement reduction factor η solves the deformation calculation problem under large displacements, but its technical solution does not involve stress calculation. In actual engineering, designers still rely on finite element simulation to estimate stress, which has the following shortcomings:

[0011] U-shaped hollow plates have different cavity structures, such as octagonal, X-shaped, and V-shaped stress distributions, making the finite element model complex and requiring separate modeling for each form.

[0012] Finite element method is expensive, time-consuming, requires highly specialized skills from designers, and the accuracy of finite element calculation results cannot be verified.

[0013] Safety hazards: Special loads, such as extreme wind pressure and snow loads, lack theoretical basis and are prone to structural failure.

[0014] III. Structural characteristics of U-shaped hollow plates:

[0015] The cross-section of the U-shaped hollow slab is a multi-layered hollow truss structure, such as... Figure 4 As shown, the thicknesses t1 and t2 of the upper and lower surface layers are much greater than those of the middle layer, and the vertical ribs are parallel to the short side span direction. This type of structure leads to:

[0016] The definition of equivalent thickness is complex: displacement equivalent thickness t weq Equivalent thickness t of stress σeq The physical meanings are different and they cannot be substituted. Since there is currently no publicly available formula for calculating the stress of a U-shaped hollow plate, and the U-shaped hollow plate is a lattice plate, the applicable range of formula ① is ω < t. Therefore, t in formula ① should be taken as the stress-equivalent thickness t of the plate. σeq However, the stress-equivalent thickness t of the plate is not yet available. σeq The calculation method. If t is taken as the equivalent thickness t of the plate displacement. weq Based on engineering experience, the maximum displacement of a plate is generally equal to the displacement equivalent thickness t. weq If the equivalent thickness is 1 to 5 times that of the stress, then using only formula ① to calculate the stress will result in serious distortion, and the equivalent thickness needs to be redefined according to the stress characteristics.

[0017] With the increasing application of U-shaped hollow panels in ultra-large span projects such as stadiums and transportation hubs, the lack of clear stress calculation formulas in the standards has become a bottleneck restricting their safety and economy. Designers urgently need a theoretically rigorous, easy-to-operate, and computationally accurate method for calculating the stress of polycarbonate U-shaped interlocking hollow panels to precisely control material strength and avoid risks or redundant designs caused by stress estimation errors. Summary of the Invention

[0018] The purpose of this invention is to provide a stress calculation method for polycarbonate U-shaped interlocking hollow panels. This method aims to solve the technical problem that neither the thin-plate stress calculation formula nor the existing displacement calculation formula can be accurately applied to stress calculation for U-shaped hollow panels, resulting in seriously distorted results.

[0019] To achieve the above objectives, the present invention adopts the following technical solution:

[0020] A method for calculating the stress of a polycarbonate U-shaped interlocking hollow panel is as follows:

[0021] Step 1: Measure and determine the basic parameters of the hollow board, including dimensional parameters, board type, form of support connection points, and load on the board.

[0022] Step 2: Determine the displacement equivalent thickness t of the hollow plate based on the dimensional parameters. weq ; Displacement equivalent thickness t weq To determine whether the stress calculation of the hollow plate considers the numerical limit of large displacement effect; when t weq When the displacement is greater than ω, the hollow plate exhibits a large displacement effect, where ω is the vertical displacement of the hollow plate, and ω is taken as the maximum displacement of the hollow plate. max ;

[0023] Step 3: Determine the stress-equivalent thickness t of the plate based on the dimensional parameters. σeq Stress equivalent thickness t σeq Determined based on the principle that the surface stress of hollow boards and equivalent solid boards is equal;

[0024] Step 4: Determine the stress adjustment coefficient η:

[0025] The formula for calculating the stress adjustment factor η is as follows:

[0026]

[0027] In the formula, a hollow board of a fixed model is selected as the test board;

[0028] σ1 represents the mid-span stress of the test plate calculated using formula ① for plate surface stress under small displacement, under different load conditions.

[0029] in,

[0030] In the formula: σ1 is the plate surface stress under small displacement, m is the stress coefficient, q is the uniformly distributed load on the plate surface, a is the width of the plate, and t is taken as t σeq , t σeq The stress-equivalent thickness of the plate;

[0031] σ2 is the mid-span stress of the test plate obtained by performing a loading test on the test plate under the same loading condition as σ1;

[0032] η is divided into tensile stress adjustment coefficient η σt and the compressive stress adjustment coefficient η σp ;

[0033] Step 5, η σt and η σp Substituting into formula ①, we obtain formulas ⑤ and ⑥, and use these to calculate and determine the stress in the hollow plate:

[0034] The stress calculation formula is as follows:

[0035]

[0036] In the formula, σ t It is under tensile stress;

[0037]

[0038] In the formula, σ p It is under compressive stress.

[0039] The basic parameters in step one include:

[0040] Dimensional parameters: width a of the hollow board, height h of the hollow board, thickness t1 of the upper surface layer, thickness t2 of the lower surface layer, and height h1 of the hollow board centroidal axis from the lower surface layer;

[0041] Plate type and support connection point form: A one-way plate with fixed hinge supports on opposite sides is adopted to determine the form of the calculation model;

[0042] The load q on the plate is equivalent to a uniformly distributed load on the plate surface.

[0043] In step two, the equivalent thickness t of the plate displacement weq The calculation formula is as follows:

[0044]

[0045] In step three, the bending stress formula for the plate is calculated according to the small deformation theory:

[0046] and We obtain that σ is proportional to h / I;

[0047] Based on the principle that the surface stress of hollow plates and equivalent solid plates are equal, the proportional conversion process is as follows, yielding formula ⑧:

[0048] In the formula, σ is the bending stress of the plate under the small deformation theory, M is the bending moment, W is the section modulus, h is the height of the hollow plate, I is the moment of inertia of the hollow plate section, and t σeq I is the equivalent thickness of a solid plate, i.e., the stress-equivalent thickness of the plate. σeqThe moment of inertia of the equivalent solid plate section;

[0049] The moment of inertia of the hollow plate section is

[0050] Let be the moment of inertia of the upper surface layer of the hollow board, and 'a' be the width of the hollow board, taken as 1 unit width.

[0051] Let be the moment of inertia of the lower surface layer of the hollow board, and 'a' be the width of the hollow board, taken as 1 unit width.

[0052] in, Relative to t1(h-h1) 2 The value is too small. relative to t2h1 2 The value is too small and will not be included in the next calculation.

[0053] The moment of inertia I of the hollow plate is obtained as follows:

[0054] The formula for the moment of inertia of the equivalent solid plate section is: b is the width of the equivalent solid plate, taken as 1 unit width, then I and I σeq Substituting into formula ⑧, we get formula ⑨:

[0055]

[0056] Formula 9 is derived to form formula 10, from which t is obtained. σeq :

[0057]

[0058] In step four, the stress adjustment coefficient η is based on ω / t, which is directly related to the displacement. σeq For parameters;

[0059] Based on the formula i for calculating the bending stiffness D of the plate and the formula ii for calculating the displacement of the plate, ω / t σeq The parameters are converted to physical parameters related to the plate's fundamental parameters. The proportional conversion process is shown in formula iii:

[0060]

[0061] In the formula: D is the bending stiffness of the plate, E is the elastic modulus of the plate, and t σeq Let φ be the stress-equivalent thickness of the plate, υ be Poisson's ratio, ω be the vertical displacement of the plate, μ be the deflection coefficient, q be the load on the plate, and a be the width of the plate.

[0062] Formula iii is based on ω and Directly proportional to D and Proportional, therefore and Proportional; the stress adjustment coefficient η is converted to... The relationship curve.

[0063] In step four, the coefficient parameter θ is introduced to convert the stress adjustment coefficient η into physical parameters related to the dimensional parameters in the basic parameters and the load on the plate.

[0064]

[0065] In the formula, q is the load on the plate, a is the width of the plate, E is the elastic modulus of the plate, and t is the elastic modulus of the plate. σeq The stress-equivalent thickness of the plate.

[0066] Based on the data of η and θ, a scatter plot is constructed. The formula for calculating the stress adjustment coefficient η using power function fitting is as follows: The tensile stress adjustment coefficient is shown in formula ③:

[0067] η σt =0.73e (-θ / 70) +0.27③,

[0068] The compressive stress adjustment factor is shown in formula ④:

[0069] η σp =0.66e (-θ / 70) +0.34④.

[0070] In step four, the material of the test plate has a Poisson's ratio υ = 0.4, an elastic modulus E = 2400 MPa, and the plate type is a one-way plate with fixed hinge supports on opposite sides.

[0071] Compared with the prior art, the present invention has the following features and beneficial effects:

[0072] This invention proposes a stress calculation formula for U-shaped hollow plates based on theoretical formulas, experimental data, and engineering experience. The invention provides a stress calculation formula for polycarbonate U-shaped hollow plates and the determination of relevant parameters within the formula. The stress calculation formula for U-shaped hollow plates is based on the small displacement calculation theory of plates, and the values ​​of basic parameters, stress equivalent thickness, bending stiffness, coefficient parameters, and stress adjustment coefficients are determined sequentially based on experimental calculation results, ultimately deriving a stress calculation formula for U-shaped hollow plates, filling a gap in the theoretical framework for stress calculation of U-shaped hollow plates.

[0073] Based on the displacement equivalent thickness in existing hollow plate displacement calculation methods, this invention proposes a stress equivalent thickness t for U-shaped hollow plates, taking into account their mechanical properties. σeq The definition is based on the classical theoretical calculations and experimental results of small plate deformation, and for the first time, the stress adjustment coefficient η for tension-compression separation is introduced.σt and η σp We obtained the stress calculation formula for the U-shaped hollow plate under the large deformation effect, thus forming a complete stress calculation system.

[0074] Traditional thin-plate theory only considers bending stress, neglecting the contribution of membrane stress to the total stress under large deformation. This invention, however, achieves an order-of-magnitude improvement in stress calculation accuracy by decoupling and correcting tensile and compressive stresses. Based on the difference in stiffness degradation of polycarbonate materials under tension and compression, an independent adjustment coefficient η is introduced. σt and η σp The stress amplification effect in the tension and compression zones is corrected separately, and the membrane stress can account for more than 60% of the total stress. The parameter θ is the physical meaning of the load to the equivalent stiffness, characterizing the degree of deformation. Through fitting experimental data, it was found that when θ > 20°, i.e., large deformation, η... σt and η σp It decreases exponentially with θ, accurately reflecting the offsetting effect of membrane stress on bending stress.

[0075] This improvement not only solves the inherent defects of traditional formulas, but also achieves a unity of theoretical accuracy and engineering practicality through experimental data fitting and parameter adjustment. It can avoid complex finite element modeling and directly calculate through formulas, providing core technical support for the standardized design of polycarbonate U-shaped locking hollow panels. Attached Figure Description

[0076] The present invention will now be described in further detail with reference to the accompanying drawings.

[0077] Figure 1 This is a schematic diagram of the U-shaped hollow plate planar arrangement and support connection points of the present invention.

[0078] Figure 2 This is a schematic diagram of a half-span cross-section structure of a U-shaped hollow slab.

[0079] Figure 3 This is a diagram showing the mid-span deformation of a U-shaped hollow plate.

[0080] Figure 4 This is a schematic diagram of the cross-sectional parameters of a U-shaped hollow plate.

[0081] Figure 5 It is σ t The figure shows the fitting formula for tensile stress versus θ.

[0082] Figure 6 It is σ p The figure shows the fitting formula between compressive stress and θ.

[0083] Figure 7 The present invention is subjected to tensile stress σ t Comparison of the formula calculation results, experimental values, and traditional thin plate stress calculation formula ①.

[0084] Figure 8 The compressive stress σ of this invention p Comparison of the formula calculation results, experimental values, and traditional thin plate stress calculation formula ①.

[0085] Figure 9 This is a schematic diagram of the test points for compressive and tensile stresses under downward load on the plate surface.

[0086] Figure 10 This is a schematic diagram of the test points for compressive and tensile stresses on the plate under upward load.

[0087] Figure 11 It is Table 1.

[0088] Figure 12 It is Table 2.

[0089] Figure 13 It is Table 3.

[0090] Figure 14 It is Table 4.

[0091] Figure reference numerals: 1 - support connection point, 2 - vertical rib, 3 - upper surface layer, 4 - lower surface layer, 5 - intermediate layer, 6 - tensile stress point, 7 - compressive stress point. Detailed Implementation

[0092] See the examples. Figure 1 As shown, this invention mainly focuses on U-shaped locking hollow panels. U-shaped locking hollow panels are a type of hollow panel; see [link to related document]. Figure 1 As shown, this refers to vertical support connection points 1 protruding from the plane of the hollow plate at both edges, with a length of L and a width of a. See the cross-section of the U-shaped hollow plate. Figure 2 As shown. The formula for calculating the stress of a thin plate ① is derived under small displacement conditions. It assumes that the plate only experiences bending stress and that in-plane membrane stress is negligible. Its applicable range is ω < t, which cannot satisfy the stress calculation for U-shaped hollow plates under large displacement effects. Since the U-shaped hollow plate is a lattice plate with multiple cavities, the applicable range t should be taken as the equivalent displacement thickness t of the plate. weq In formula ①, t should be taken as the stress equivalent thickness t of the plate. σeq Therefore, this invention proposes a stress calculation method for a polycarbonate U-shaped locking hollow board. The calculation method is as follows: Step 1, measure and determine the basic parameters of the hollow board, including dimensional parameters, board type, form of support connection points and load on the board.

[0093] The basic parameters in step one include:

[0094] Dimensional parameters: width a of the hollow board, height h of the hollow board, thickness t1 of the upper surface layer, thickness t2 of the lower surface layer, and height h1 of the hollow board centroidal axis from the lower surface layer.

[0095] Plate type and support connection point form: A one-way plate with fixed hinge supports on opposite sides is used to determine the form of the calculation model.

[0096] The load q on the plate is equivalent to a uniformly distributed load on the plate surface.

[0097] Step 2: Determine the displacement equivalent thickness t of the hollow plate based on the dimensional parameters in Step 1. weq ; Displacement equivalent thickness t weq To determine whether the stress calculation of the hollow plate considers the numerical limit of large displacement effect; when t weq When the displacement is greater than ω, the hollow plate exhibits a large displacement effect, where ω is the vertical displacement of the hollow plate, and ω is taken as the maximum displacement of the hollow plate. max .

[0098] The cross-section of the hollow plate is an umbo-shaped cavity, from which the displacement equivalent thickness t is derived. weq It is related to the dimensions of the upper and lower surface layers.

[0099] The plan layout and support connection points of the hollow slab are as follows: Figure 1 As shown in the figure, L is the direction of the long side of the plate, i.e., the rib, and a is the width of the plate.

[0100] At this point, the displacement equivalent thickness t of the hollow plate is determined. weq .

[0101] The cross-sectional structure of the actual hollow board is as follows: Figure 2 As shown, the cavity in the cross-section of the figure is shaped like an opening, similar to a hollow truss structure. The thickness of the upper surface layer 3 and the lower surface layer 4 varies among different brands, but generally falls between 0.6mm and 0.9mm. The thickness of the middle layer 4 is generally between 0.15mm and 0.2mm. See also Figure 3 As shown, the deformation diagram basically conforms to the plane section assumption, the effect of shear can be ignored, the deformation between layers can be coordinated and consistent, and the relative sliding between layers can be ignored.

[0102] Generally, the thickness of the upper and lower surface layers is 3 to 6 times that of the intermediate layer, and the upper and lower surface layers are furthest from the neutral axis. Vertical rib 2 is perpendicular to the short-span direction of the plate. (See [reference]). Figure 4 As shown. Therefore, the displacement equivalent thickness t weq The calculation formula is simplified to only consider the influence of the upper and lower surface layers, and the equivalent thickness calculation formula can be applied to hollow plates with different cavities.

[0103] The equivalent thickness t of the plate displacement weq The calculation formula is as follows:

[0104]

[0105] Step 3: Determine the stress-equivalent thickness t of the plate based on the dimensional parameters in Step 1. σeq Stress equivalent thickness t σeq The determination is based on the principle that the surface stress of hollow boards and equivalent solid boards are equal.

[0106] In step three, the bending stress formula for the plate is calculated according to the small deformation theory:

[0107] and We obtain that σ is proportional to h / I;

[0108] Based on the principle that the surface stress of hollow plates and equivalent solid plates are equal, the proportional conversion process is as follows, yielding formula ⑧:

[0109] In the formula, σ is the bending stress of the plate under the small deformation theory, M is the bending moment, W is the section modulus, h is the height of the hollow plate, I is the moment of inertia of the hollow plate section, and t σeq I is the equivalent thickness of a solid plate, i.e., the stress-equivalent thickness of the plate. σeq The moment of inertia of the equivalent solid plate section;

[0110] The moment of inertia of the hollow plate section is

[0111] Let be the moment of inertia of the upper surface layer of the hollow board, and 'a' be the width of the hollow board, taken as 1 unit width.

[0112] Let be the moment of inertia of the lower surface layer of the hollow board, and 'a' be the width of the hollow board, taken as 1 unit width.

[0113] in, Relative to t1(h-h1) 2 The value is too small. relative to t2h1 2 The value is too small and will not be included in the next calculation.

[0114] The moment of inertia I of the hollow plate is obtained as follows:

[0115] Formula for the moment of inertia of the equivalent solid plate section b is the width of the equivalent solid plate, taken as 1 unit width, then I and I σeq Substituting into formula ⑧, we get formula ⑨:

[0116]

[0117] Formula 9 is derived to form formula 10:

[0118]

[0119] Step 4: Determine the stress adjustment coefficient η:

[0120] Step a, the stress adjustment coefficient η is ω / t, which is directly related to the displacement. σeq For parameters,

[0121] The stress adjustment coefficient η is derived. Proportional relationship:

[0122] Based on the formula i for calculating the bending stiffness D of the plate and the formula ii for calculating the displacement of the plate, ω / t σeq The parameters are converted to physical parameters related to the plate's fundamental parameters. The proportional conversion process is shown in formula iii:

[0123]

[0124] In the formula: D is the bending stiffness of the plate, E is the elastic modulus of the plate, and t σeq Let φ be the stress-equivalent thickness of the plate, υ be Poisson's ratio, ω be the vertical displacement of the plate, μ be the deflection coefficient, q be the load on the plate, and a be the width of the plate.

[0125] Formula iii is based on ω and Directly proportional to D and Proportional, therefore and Proportional; the stress adjustment coefficient η is converted to... The relationship curve.

[0126] Step b, introduce the coefficient parameter θ, and convert the stress adjustment coefficient η into physical parameters related to the dimensional parameters in the basic parameters and the loads on the plate:

[0127]

[0128] In the formula, q is the load on the plate, a is the width of the plate, E is the elastic modulus of the plate, and t is the elastic modulus of the plate. σeq The stress-equivalent thickness of the plate.

[0129] Step c, the formula for calculating the stress adjustment coefficient η is as follows:

[0130]

[0131] In the formula, based on the test data of the hollow board manufacturer, the material's Poisson's ratio υ = 0.4, elastic modulus E = 2400 MPa, and the board type is a one-way board with fixed hinge supports on opposite sides as the test board;

[0132] σ1 represents the mid-span stress of the test plate calculated using the plate surface stress calculation formula ① under different load conditions.

[0133] in,

[0134] In the formula: σ is the plate surface stress under small displacement, m is the stress coefficient, q is the uniformly distributed load on the plate surface, a is the width of the plate, and t is taken as t σeq , t σeq The stress-equivalent thickness of the plate;

[0135] σ2 is the mid-span stress of the test plate obtained by performing a loading test on the test plate under the same load condition as σ1.

[0136] See Figure 9-10 As shown, η is related to the stress direction on the plate surface, and can be divided into tensile stress and compressive stress.

[0137] Theoretical analysis shows that, under the small deformation theory, the stress calculation formula for a plate is: Under the small deformation theory, the compressive stress and tensile stress on the upper and lower surfaces of the plate are equal. However, when considering the large displacement effect, under the large deformation theory, the membrane stress of the plate is taken into account, resulting in tensile stress across the entire cross-section of the plate. This increases the tensile stress and decreases the compressive stress. The simplified stress calculation formula should be: Therefore, stress calculations that take into account the effects of large deformations need to distinguish between tensile stress and compressive stress in order to obtain more accurate stress values.

[0138] The specific experimental and calculation process is as follows:

[0139] For the calculation of η and θ, please refer to [link / reference]. Figure 11 Table 1 and Figure 12 As shown in Table 2.

[0140] Step d: Then, fit the formula for calculating the stress adjustment coefficient η to a power function formula related to the coefficient parameter θ; create a scatter plot of the η vs. θ data in Tables 1 and 2. Based on the above data, see [reference needed]. Figure 5 and Figure 6 As shown, η gradually decreases as θ increases. The formula for calculating the stress adjustment coefficient using power function fitting is as follows:

[0141] The tensile stress adjustment factor is shown in formula ③:

[0142] η σt =0.73e (-θ / 70) +0.27③,

[0143] In the formula, η σt This is the tensile stress adjustment factor;

[0144] The compressive stress adjustment factor is shown in formula ④:

[0145] η σp =0.66e (-θ / 70) +0.34④,

[0146] In the formula, η σp This is the adjustment coefficient for compressive stress.

[0147] R in this formula 2 Values ​​and adjusted R 2 The values ​​are all greater than 0.95, indicating a very good fit to the formula. R0 2 R is the coefficient of determination, a statistic that measures the goodness of fit, which refers to how well the regression line fits the observed values. 2 The closer the value is to 1, the better the regression line fits the observed values.

[0148] Based on the classical theoretical calculations and experimental results for small deformation of plates, a stress reduction factor η is introduced to obtain the stress calculation formula for hollow plates under large deformation conditions. The stress reduction factor η is only related to the parameter θ, which in turn depends only on the plate's own parameters.

[0149] Step 5, η σt and η σp Substituting into formula ①, we obtain formulas ⑤ and ⑥, and use these to calculate and determine the stress in the hollow plate:

[0150] The stress calculation formula used is as follows:

[0151]

[0152] In the formula, σ t It is under tensile stress;

[0153]

[0154] In the formula, σ p It is under compressive stress.

[0155] To illustrate the accuracy of the formula, the results of calculations using formulas ⑤ and ⑥, experimental values, and a comparison with the traditional thin plate stress calculation formula ① are provided below. Figure 7-8 As shown. Figure 7 The data results corresponding to the tensile stress in the middle are as follows Figure 13 As shown in Table 3. Figure 8 The data results corresponding to the compressive stress in the middle are as follows Figure 14 As shown in Table 4.

[0156] As shown in the figure, when θ≤20, the calculation results of several methods are not much different from the experimental results, because the value of θ is relatively small and the in-plane film stress is not obvious. As the value of θ increases, the difference between the calculation result of formula ① and the experimental value becomes larger and larger.

Claims

1. A method of stress calculation for a polycarbonate u-lock hollow panel, characterized by, The calculation method is as follows: Step one, measure and determine the basic parameters of the hollow plate, the basic parameters including size parameters, plate type, form of support connection point and load borne by the plate body; Step two, according to the size parameter, determine the displacement equivalent thickness t of the hollow plate weq ; displacement equivalent thickness t weq is the numerical limit for judging whether the stress calculation of the hollow plate considers large displacement effect; when t weq > ω, the hollow plate has large displacement effect, where ω is the vertical displacement of the hollow plate, and ω takes the maximum displacement ω max of the hollow plate Step three, according to the size parameter, determine the stress equivalent thickness t of the plate σeq ; stress equivalent thickness t σeq According to the principle of equal plate surface stress of hollow plate and equivalent solid plate Step four, determine the stress adjustment coefficient η: The calculation formula of the stress adjustment coefficient η is as follows: In the formula, a fixed model of hollow plate is selected as the test plate; σ1 is the stress in the middle of the plate span calculated by the plate surface stress calculation formula ① under small displacement of the test plate under different load conditions, wherein, where σ1 is the plate surface stress at small displacement, m is the stress coefficient, q is the plate surface uniform load, a is the plate width, t is the plate thickness, and t is the stress equivalent thickness of the plate. σeq σeq ​​ σ2 is the stress in the middle of the plate span obtained by the same loading test as σ1 load condition on the test plate; η is divided into a tensile stress adjustment coefficient η σt and a compressive stress adjustment coefficient η σp ; Step five, η σt and η σp are brought into formula ① respectively, to get formula ⑤ and ⑥, and the stress of hollow plate is calculated and determined: The stress calculation formula is as follows: wherein σ t is a tensile stress; In the formula, σ p It is under compressive stress.

2. The stress calculation method of the polycarbonate U-shaped lock hollow plate according to claim 1, characterized in that: The basic parameters in step one include: Size parameters: width a of the hollow plate, height h of the hollow plate, thickness t1 of the upper surface layer, thickness t2 of the lower surface layer and height h1 of the hollow plate centroid from the lower surface layer; Plate type and form of support connection point: single-way plate with opposite edge fixed hinged support, and then determine the form of the calculation model; Load borne by the plate body q: equivalent to uniform plate surface load.

3. The stress calculation method of the polycarbonate U-shaped lock hollow plate according to claim 2, characterized in that: In step two, the displacement equivalent thickness t of the plate weq is calculated as follows:

4. The stress calculation method of the polycarbonate U-shaped lock hollow plate according to claim 3, characterized in that: In step three, according to the bending stress formula of the plate under small deformation theory: and σ is proportional to h / I; According to the principle of equal plate surface stress of hollow plate and equivalent solid plate, the proportional conversion process is as follows, and formula 7 is obtained: where σ is the bending stress of the plate under small deformation theory, M is the bending moment, W is the section modulus, h is the height of the hollow plate, I is the section moment of inertia of the hollow plate, t σeq is the thickness of the equivalent solid plate, i.e., the stress equivalent thickness of the plate, I σeq is the section moment of inertia of the equivalent solid plate. The hollow plate cross-sectional moment of inertia is for the upper surface layer of the hollow plate, a is the width of the hollow plate, taking 1 as the unit width; for the lower surface layer of the hollow plate, a is the width of the hollow plate, and is taken as 1 for unit width; Wherein, Relative t1(h-h1) 2 The value is too small, Relative t2h1 2 The value is too small, not included in the next step calculation; The cross-sectional moment of inertia I of the hollow plate is obtained as: The cross-sectional moment of inertia formula of the equivalent solid plate is: b is the width of the equivalent solid plate, which is taken as 1 unit width, and then I and I σeq Substitute formula ⑧ into formula ⑨ to obtain formula ⑨: Equation (9) is derived to obtain equation (10) to obtain t σeq :

5. The stress calculation method of the polycarbonate U-shaped lock hollow plate according to claim 4, characterized in that: In step four, the stress adjustment factor η is ω / t, which considers the direct relationship with displacement σeq is a parameter; According to the calculation formula i of the bending stiffness D of the plate and the displacement calculation formula ii of the plate, ω / t σeq is converted into a physical parameter related to the basic parameters of the plate, and the proportional conversion process is shown in formula iii: where D is the bending stiffness of the plate, E is the modulus of elasticity of the plate, t σeq is the stress equivalent thickness of the plate, υ is the Poisson's ratio, ω is the vertical displacement of the plate, μ is the deflection coefficient, q is the load on the plate, and a is the width of the plate. Equation III is based on the fact that ω is proportional to D is proportional to Therefore is proportional to The stress adjustment factor η is transformed into a relationship curve with .

6. The stress calculation method of the polycarbonate U-shaped lock hollow plate according to claim 5, characterized in that: In step four, introduce the coefficient parameter θ to convert the stress adjustment coefficient η into a physical parameter related to the size parameters in the basic parameters and the load borne by the plate body; where q is the load on the plate, a is the width of the plate, E is the modulus of elasticity of the plate, t is the thickness of the plate, and σeq is the stress equivalent thickness of the plate.

7. The stress calculation method of the polycarbonate U-shaped lock hollow plate according to claim 6, characterized in that: According to the data of η and θ, a scatter plot is established, and the calculation formula of the stress adjustment coefficient η using power function fitting is as follows: The tensile stress adjustment coefficient is shown in formula ③: η σt = 0.73e (-θ / 70) + 0.27θ, The compressive stress adjustment coefficient is shown in formula ④: η σp = 0.66e (-θ / 70) + 0.34f.

8. The method of stress calculation for polycarbonate u-lock hollow panels according to claim 1, characterized in that: In step four, the Poisson's ratio υ of the material of the test plate is 0.4, the elastic modulus E is 2400 Mpa, and the plate type is single-way plate with opposite edge fixed hinged support.

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