A method for predicting the fatigue life of a welded structure based on harmonic response structural stress

Abstract

The application discloses a kind of welded structure harmonic response structural stress fatigue life prediction method, comprising the following steps: step 1: build the finite element model of welded structure containing weld;Step 2: using unit external load to the finite element model of welded structure harmonic sweep frequency obtains node response displacement;Step 3: according to external load coefficient obtains the unit stiffness matrix and node displacement under external load, as follows: step 4: calculate the simple harmonic response structural stress and equivalent structural stress of structure.The welded structure harmonic response structural stress fatigue life prediction method of the application: (1) compared with traditional quasi-static method, can solve the problem that quasi-static method cannot be carried out vibration fatigue evaluation, (2) compared with frequency domain structural stress method, can solve the problem that frequency domain structural stress method cannot evaluate simple harmonic vibration fatigue, (3) compared with traditional transient structural stress method, the method of the application is more efficient, and the result error is very small.

Description

Technical Field

[0001] This invention relates to the fields of mechanical and engineering technology, and more particularly to the field of welded structure life assessment technology. Background Technology

[0002] Simple harmonic vibrations are common in mechanical or engineering structures such as rotating equipment, transmission mechanisms, test benches, and components affected by eddy currents, including engines, pumps, turbine blades, and bridges. These vibrations have a significant impact on the fatigue life of welded structures. Long-term vibrations can cause fatigue damage to structural components, greatly reducing the safety and reliability of the structure, affecting its service life, and in severe cases, endangering people's lives and property.

[0003] In the past decade, scholars at home and abroad have conducted extensive research on fatigue life assessment of welded structures. For example, reference (1): Zhao Wenzhong, Li Xiangwei, Dong Pingsha. Theory and Method of Fatigue-Resistant Design of Welded Structures [M]. Beijing: Machinery Industry Press, 2017. Reference (2): BS7608-1993, Code of practice for fatigue design and assessment of steel structures [S]. England: British Standard Institute, 1993. The structural stress method is an effective method for evaluating welded structures because it is insensitive to finite element meshes and has only one SN curve, which can be applied to any type of welded joint. It has become the fatigue assessment standard in the American ASME standard and has been widely used in engineering. However, at present, most of this method is limited to calculation using quasi-static methods. Under the vibration state of welded structures, the traditional dynamic structural stress fatigue analysis methods mainly include three calculation methods: transient time domain method, modal method and frequency domain method. The transient time domain method can usually obtain relatively accurate cumulative damage analysis accuracy, but it involves a long calculation time and a large calculation cost. The modal method has the limitation of insufficient effective mass coefficient and calculation result accuracy due to the consideration of modes. Frequency domain fatigue prediction methods can significantly reduce the computation time of transient simulation analysis and provide more complete response information. However, existing frequency domain methods for structural stress, which use PSD random vibration as input and response and employ the Dirlik method for statistical analysis, are suitable for steady-state random vibration. Due to the limitations of Dirlik in narrowband statistics, it is difficult to perform fatigue assessment of simple harmonic vibration.

[0004] Therefore, since the traditional structural stress method is insufficient for assessing simple harmonic vibration fatigue, there is an urgent need to research new methods for predicting the fatigue life of simple harmonic vibration and to evaluate the fatigue life of welded structures excited by simple harmonic waves. This has significant theoretical and practical engineering implications for the fatigue resistance design, fatigue experimental evaluation, and fatigue test scheme development of welded structures subjected to simple harmonic vibration. Summary of the Invention

[0005] To address the aforementioned problems in traditional fatigue life assessment methods for welded structures, this invention provides a method for predicting the structural stress fatigue life of welded structures based on harmonic response.

[0006] The technical solution adopted by the present invention to achieve the above objectives is: a method for predicting the structural stress fatigue life of welded structures based on harmonic response, comprising the following steps:

[0007] Step 1: Construct a finite element model of the welded structure including the weld seam, as follows:

[0008] 1-1: The geometric model of the welded structure is meshed using the finite element method, with 2D or 3D elements used for the mesh;

[0009] 1-2: Construct the calculated weld, and define the elements and weld toe nodes in the form of weld toe or weld root according to the traditional structural stress method;

[0010] Step 2: Perform harmonic frequency sweep on the finite element model of the welded structure using a unit external load to obtain the nodal response displacements, as detailed below:

[0011] Structural vibration harmonic response analysis involves analyzing the vibration of a structure under harmonic excitation to solve for its vibration response. For a multi-degree-of-freedom system, the dynamic equation with harmonic excitation can be written as:

[0012]

[0013] In the formula: [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. It is an acceleration vector. {x} is a velocity vector, and {P(ω)}e iωt It is an external load, such as acceleration, force, and velocity, etc., {P(ω)} is the complex vector of the external load, e iωt This is a time-domain term, where ω is the angular frequency of the applied load.

[0014] Therefore, let the vibration response displacement be {u(ω)}, then we have:

[0015] {x}={u(ω)}e iωt (20)

[0016] In the formula, u(ω) is the displacement vector, which can be obtained from equation (2):

[0017]

[0018]

[0019] Substituting (2), (3), and (4) into equation (1), we get:

[0020] ([K]-ω 2 [M]+iω[C]){u(ω)}={P(ω)} (23)

[0021] Therefore, equation (5) is the harmonic excitation equation with frequency ω, and {u(ω)} is the unit external load displacement response vector of the structure. According to equation (5), with unit simple harmonic load, frequency sweep calculation is performed using the complete method or modal method, and the harmonic response displacement {u(ω)} of each node at each frequency is obtained by finite element software.

[0022] Step 3: Obtain the element stiffness matrix and nodal displacements under external loads based on the external load coefficients, as detailed below:

[0023] The element nodal forces of the actual load are:

[0024] {F e (ω)}=[K e ][λ]{u(ω)}=[K e ]{u e (ω)} (24)

[0025] In the formula [K e ] is the element stiffness matrix, {u e (ω)} is the displacement matrix of the corresponding element, [λ] is the external load coefficient matrix, that is, the multiple matrix of the actual load to the unit load, {F e (ω)} represents the nodal force matrix. The element stiffness matrix and nodal displacements under external loads are obtained based on the external load coefficient. These are multiplied to obtain the nodal forces at the weld toe or weld root section, and then the moments are derived. The nodal forces and moments of adjacent elements are combined to obtain the nodal forces {F} of the node in its local coordinate system. i (ω)} and nodal torque response {M i (ω)};

[0026] Step 4: Calculate the harmonic response structural stress and equivalent structural stress of the structure. Use Miner's linear damage accumulation theory and the master SN curve to obtain the fatigue life of the structural welds, as detailed below:

[0027] 4-1: Calculate the structural stress and equivalent structural stress of the structure.

[0028] The structural stress is calculated by transforming the nodal force coordinates and calculating the membrane stress and bending stress, as shown in formulas (7) and (8).

[0029]

[0030]

[0031] In the above formula, σ s (ω), σ m (ω), σ b (ω), F iy (ω) are the harmonic response vectors of structural stress, membrane stress, bending stress, and nodal force in the direction perpendicular to the weld toe line on the mid-thickness surface of the plate, respectively. ix (ω) is the bending moment harmonic response vector along the weld toe line on the thick surface of the weld plate, τ s (ω), τ m (ω), τ b (ω), F ix (ω) are the harmonic response vectors of shear structural stress, shear membrane stress, shear bending stress, and shear nodal force along the weld toe direction on the mid-thickness surface of the plate, respectively. iy (ω) is the bending moment harmonic response vector of the weld plate in the direction perpendicular to the weld toe line, t is the plate thickness, and L is the distance matrix between nodes in the weld thickness section in the structural stress method.

[0032] Define the response load ratio correction factor:

[0033]

[0034]

[0035] Under load control conditions, it is equation (11); under displacement control conditions, it is equation (12):

[0036]

[0037]

[0038] r = r s (ω) or r = r τ (ω) (30)

[0039] Let r be a dimensionless function of the bending ratio r under harmonic load.

[0040] The equivalent structural stress at each node at each frequency is obtained, as shown in formulas (14) and (15):

[0041]

[0042]

[0043] In the above formula, △S s (ω) represents the range of equivalent structural stress variation in the harmonic response perpendicular to the weld toe on the neutral plane of the weld thickness, ΔS. τ (ω) represents the range of equivalent structural stress variation along the weld toe line on the thick surface of the weld plate, where m is a constant; I(rs (ω)), I(r) τ (ω)) refers to the dimensionless function of the bending ratio r of the stress load of the harmonic structure and the stress load of the harmonic shear structure, respectively, which is obtained by substituting (13) into (11) and (12). Thus, the equivalent structural stress vector can be obtained through equations (14) and (15), that is, the equivalent structural stress amplitude and phase of the weld toe node at frequency ω are obtained;

[0044] When △S τ (ω)>△S s (ω) / 3

[0045]

[0046] otherwise

[0047] △S e (ω)=△S s (ω) (34)

[0048] β is a constant representing the ratio of fatigue strength between the normal stress based on fatigue testing and the shear stress based on testing.

[0049] △S e (ω) represents the range of equivalent structural stress variation in the nodal harmonic response;

[0050] 4-2: Fatigue life of structural welds under simple harmonic vibration is obtained using Miner's linear damage accumulation theory and the master SN curve:

[0051] The harmonic response of each node is equivalent to the structural stress ΔS. e (ω) forms a response spectrum, if the range of the equivalent structural stress of the i-th order (i=1,2…k) is ΔS ei The number of iterations is n i ,

[0052] Substituting the response spectrum into the calculation formula yields the fatigue life cycle count for this level of failure:

[0053] N i =(△S) ei / C d ) 1 / h (35)

[0054] In the formula: C d and h are the experimental constants of the structural stress method, N i For △S ei The number of fatigue life cycles of the lower welded joint;

[0055] The fatigue life of this weld can be predicted, and the cumulative fatigue damage ratio is:

[0056]

[0057] In step 4-1, m is a constant of 3.6.

[0058] In step 4-2, if statistical fatigue response spectral density is required, the numerical square of the displacement response spectrum is further converted into a density spectrum, and the S-value is statistically analyzed using the NarrowBand, Sterinberg, Dirlik, or Lalananne methods. e (ω) Density spectrum fatigue.

[0059] The method for predicting the structural stress fatigue life of welded structures based on harmonic response of the present invention has the following advantages: (1) Compared with the traditional quasi-static method, it can solve the problem that the quasi-static method cannot perform vibration fatigue assessment, obtain the structural stress under simple harmonic vibration, and perform fatigue life assessment. (2) Compared with the frequency domain structural stress method, it can solve the problem that the frequency domain structural stress method cannot assess simple harmonic vibration fatigue, better analyze the response generated by simple harmonic vibration, obtain the final result of displacement, and the assessment result is more accurate than that of the frequency domain structural stress method. (3) Compared with the traditional transient structural stress method, the method of the present invention is more efficient and has a very small result error. The efficiency of obtaining the response by sweeping the simple harmonic frequency using the method of the present invention is much higher than the efficiency of obtaining the structural stress response by simulating the transient frequency of a single frequency band. By using the method of the present invention to evaluate fatigue tests, the number of simple harmonic fatigue tests and costs can be effectively reduced, and time can be saved significantly. Therefore, the present invention has important theoretical research and practical significance for the fatigue resistance design of welded structures. Attached Figure Description

[0060] Figure 1 Flowchart of the method for predicting the harmonic response structural stress fatigue life of welded structures according to the present invention;

[0061] Figure 2 It is a finite element model of a T-type welded joint containing weld seams;

[0062] Figure 3 This is a comparison of weld fatigue damage using the harmonic response method, transient method, and frequency domain method. Detailed Implementation

[0063] like Figure 1 As shown, the present invention provides a method for predicting the structural stress fatigue life of a welded structure based on harmonic response, comprising the following steps:

[0064] Step 1: Construct a finite element model of the welded structure including the weld seam, as follows:

[0065] 1-1: The geometric model of the welded structure is meshed using the finite element method, with 2D or 3D elements used for the mesh;

[0066] 1-2: Constructing the calculated weld. Define elements and weld toe nodes in the form of weld toes or weld roots according to traditional structural stress methods.

[0067] Step 2: Perform harmonic frequency sweep on the finite element model of the welded structure using a unit external load to obtain the nodal response displacements, as detailed below:

[0068] Structural vibration harmonic response analysis involves analyzing the vibration of a structure under harmonic excitation to determine its vibration response. For a multi-degree-of-freedom system, the general form of its dynamic equations with harmonic excitation can be written as:

[0069]

[0070] In the formula: [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. It is an acceleration vector. {x} is a velocity vector, and {P(ω)}e iωt It is an external load, such as acceleration, force, and velocity, etc., {P(ω)} is the complex vector of the external load, e iωt This is a time-domain term, where ω is the angular frequency of the applied load.

[0071] Therefore, let the vibration response displacement be {u(ω)}, then we have:

[0072] {x}={u(ω)}e iωt (38)

[0073] In the formula, u(ω) is the displacement vector, which can be obtained from equation (2):

[0074]

[0075]

[0076] Substituting (2), (3), and (4) into equation (1), we get:

[0077] ([K]-ω 2 [M]+iω[C]){u(ω)}={P(ω)} (41)

[0078] Therefore, equation (5) is the harmonic excitation equation with frequency ω, and {u(ω)} is the unit external load displacement response vector of the structure. According to (5), with a unit harmonic load, frequency sweep calculation is performed using the complete method or modal method, and the harmonic response displacement {u(ω)} of each node at each frequency is obtained by finite element software.

[0079] Step 3: Obtain the element stiffness matrix and nodal displacements under external loads based on the external load coefficients, as detailed below:

[0080] After obtaining the nodal harmonic response displacement {u(ω)} under unit load through frequency sweep calculation, the nodal force under actual load is:

[0081] {Fe (ω)}=[K e ][λ]{u(ω)}=[K e ]{u e (ω)} (42)

[0082] In the formula [K e ] is the element stiffness matrix, {u e (ω)} is the displacement matrix of the corresponding element, [λ] is the external load coefficient matrix, that is, the multiple matrix of the actual load to the unit load, {F e (ω)} represents the nodal force matrix. The element stiffness matrix and nodal displacements under external loads are obtained from the external load coefficient. These are then multiplied to obtain the nodal forces at the weld toe or weld root section, and subsequently, the moments. The nodal forces and moments of adjacent elements are combined to obtain the nodal forces {F} of the node in its local coordinate system. i (ω)} and nodal torque response {M i (ω)}.

[0083] Step 4: Calculate the harmonic response structural stress and equivalent structural stress of the structure. Use Miner's linear damage accumulation theory and the master SN curve to obtain the fatigue life of the structural welds, as detailed below:

[0084] 4-1: Calculate the structural stress and equivalent structural stress of the structure.

[0085] The structural stress is calculated by transforming the nodal force coordinates and calculating the membrane stress and bending stress, as shown in formulas (7) and (8).

[0086]

[0087]

[0088] In the above formula, σ s (ω), σ m (ω), σ b (ω), F iy (ω) are the harmonic response vectors of structural stress, membrane stress, bending stress, and nodal force in the direction perpendicular to the weld toe line on the mid-thickness surface of the plate, respectively. ix (ω) is the bending moment harmonic response vector along the weld toe line on the thick surface of the weld plate, τ s (ω), τ m (ω), τ b (ω), F ix (ω) are the harmonic response vectors of shear structural stress, shear membrane stress, shear bending stress, and shear nodal force along the weld toe direction on the mid-thickness surface of the plate, respectively. iy(ω) is the bending moment harmonic response vector in the direction perpendicular to the weld toe line on the middle surface of the weld plate, t is the plate thickness, and L is the distance matrix between nodes on the middle surface of the weld thickness section in the structural stress method.

[0089] Define the response load ratio correction factor:

[0090]

[0091]

[0092] Under load control conditions, it is equation (11); under displacement control conditions, it is equation (12):

[0093]

[0094]

[0095] r = r s (ω) or r = r τ (ω) (49)

[0096] The equivalent structural stress at each node at each frequency is obtained, as shown in formulas (14) and (15).

[0097]

[0098]

[0099] In the above formula, △S s (ω) represents the range of equivalent structural stress variation in the harmonic response perpendicular to the weld toe on the neutral plane of the weld thickness, ΔS. τ (ω) is the range of equivalent structural stress variation of the harmonic response along the weld toe line on the thick surface of the weld plate, and m is a constant of 3.6; thus, the equivalent structural stress vector can be obtained through equations (14) and (15), that is, the amplitude and phase of the equivalent structural stress of the weld toe node at frequency ω are obtained.

[0100] When △S τ (ω)>△S s (ω) / 3

[0101]

[0102] otherwise

[0103] △S e (ω)=△S s (ω) (53)

[0104] β is a constant representing the ratio of fatigue strength between the normal stress based on fatigue testing and the shear stress based on testing.

[0105] △Se (ω) represents the range of equivalent structural stress variation in the nodal harmonic response;

[0106] 4-2: The fatigue life of structural welds under simple harmonic vibration is obtained by using Miner's linear damage accumulation theory and the main SN curve.

[0107] The harmonic response of each node is equivalent to the structural stress ΔS. e (ω) forms a response spectrum. If the equivalent structural stress range of the i-th order (i = 1, 2…k) is ΔS ei The number of iterations is n i ;

[0108] Substituting the response spectrum into the calculation formula yields the fatigue life cycle count for this level of failure:

[0109] N i =(△S) ei / C d ) 1 / h (54)

[0110] In the formula: C d and h are experimental constants for the structural stress method. N i For △S ei The number of fatigue life cycles of the lower welded joint;

[0111] The fatigue life of this weld can be predicted, and the cumulative fatigue damage ratio is:

[0112]

[0113] If statistical fatigue response density is required, the numerical square of the displacement response spectrum can be further converted into a density spectrum, and the S-value can be statistically analyzed using the NarrowBand, Sterinberg, Dirlik, or Lalananne methods. e (ω) Density spectrum fatigue.

[0114] In this embodiment, taking the simple harmonic vibration fatigue assessment of a T-shaped welded structure as an example, quadrilateral shell elements are used for mesh generation, and finite element software such as ANSYS is used for simulation. Figure 2 As shown.

[0115] Constraints were applied to one side of the T-shaped welded joint base plate, and simple harmonic acceleration loads of 10Hz and 100Hz were applied in the y-direction at the midpoint of the other side of the base plate, respectively. A complete method transient simulation analysis was performed. The acceleration time history was applied to the foundation using the large mass method for transient simulation. Simultaneously, a complete method harmonic response analysis was performed on the T-shaped welded joint, with a unit simple harmonic load applied in the y-direction for frequency sweep calculation. Furthermore, random vibration analysis was performed on the T-weld model. Random vibration follows probabilistic statistical laws and can only be described using probabilistic statistical methods. The finite element software used density spectrum as the load input for random vibration analysis, and PSD power spectral density was used for random vibration analysis. Since the transient method has higher accuracy, the transient fatigue life was used as the benchmark, and the fatigue life of the harmonic response method and the frequency domain method were compared. The fatigue life calculation results of the joint weld toe are shown in Table 1 and... Figure 3 As shown.

[0116] Table 1. Comparison of lifetime prediction errors between the harmonic response method of this invention and traditional methods.

[0117]

[0118] From Table 1, Figure 3 It can be seen that the fatigue life assessment results of the harmonic response method and the transient complete method have very small errors and are almost identical, indicating that the method of the present invention is effective in assessing the life of simple harmonic vibrations. The frequency domain method, due to its use of the Dirlik statistical algorithm, has a larger error in assessing simple harmonic vibrations. The harmonic response method provides a more accurate assessment result than the frequency domain structural stress method, fully demonstrating that the harmonic response can better reflect the response of simple harmonic vibrations and overcomes the shortcomings of the frequency domain method. Furthermore, the use of the complete method for frequency sweeping overcomes the deficiency of modal effective mass in the modal structural stress method.

[0119] Although the transient method yields good evaluation results, the simulation time cost is very high. Table 2 compares the time consumption of the transient method and the harmonic response method for evaluating the simple harmonic vibration fatigue of the T-type model at two frequencies.

[0120] Table 2 Comparison of calculation time for a single frequency using the harmonic response method and the transient structural stress method of this invention.

[0121] frequency Transient complete method time (s) Harmonic response method time (s) The proportion of harmonic response method and transient method 10Hz 11 1.2 10.9％ 100Hz 110 13.5 12.3％

[0122] As shown in Table 2, at a frequency of 10Hz, the harmonic response method takes 10.9% of the simulation time of the transient full method, and 12.3% at 100Hz. Analysis indicates that the harmonic response method saves more than 85% of the time compared to the transient full method, significantly improving simulation efficiency. Table 2 only evaluates two frequencies. If evaluating simple harmonic responses in the 0-100Hz frequency band, the method of this invention offers convenient frequency sweeping and very short computation time, as illustrated by the two examples above. Therefore, it is evident that applying the method of this invention to the simulation evaluation of large and complex welded structures will significantly reduce time costs.

[0123] This invention solves the problems of traditional quasi-static structural stress methods and frequency domain methods being unable to evaluate the fatigue life of simple harmonic vibrations, overcomes the shortcomings of modal effective mass in modal structural stress methods, and addresses the high time cost of transient simple harmonic vibration simulation. It improves the efficiency of harmonic simulation analysis and has significant theoretical and practical implications for the fatigue resistance design of welded structures. The method proposed in this invention is applicable to various welded structures, providing new ideas and methods for the fatigue resistance design of welded structures.

[0124] This invention has been described through embodiments. Those skilled in the art will understand that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this invention.

Claims

1. A method for predicting the stress fatigue life of a welded structure based on its harmonic response, characterized in that: Includes the following steps: Step 1: Construct a finite element model of the welded structure including the weld seam, as follows: 1-1: The geometric model of the welded structure is meshed using the finite element method, with 2D or 3D elements used for the mesh; 1-2: Construct the calculated weld, and define the elements and weld toe nodes in the form of weld toe or weld root according to the traditional structural stress method; Step 2: Perform harmonic frequency sweep on the finite element model of the welded structure using a unit external load to obtain the nodal response displacements, as detailed below: Structural vibration harmonic response analysis involves analyzing the vibration of a structure under harmonic excitation to solve for its vibration response. For a multi-degree-of-freedom system, the dynamic equation with harmonic excitation can be written as: In the formula: [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. It is an acceleration vector. {x} is a velocity vector, and {P(ω)}e iωt It is the external load, {P(ω)} is the complex vector of the external load, e iωt This is a time-domain term, where ω is the angular frequency of the applied load. Therefore, let the vibration response displacement be {u(ω)}, then we have: {x}={u(ω)}e iωt (2) In the formula, u(ω) is the displacement vector, which can be obtained from equation (2): Substituting (2), (3), and (4) into equation (1), we get: ([K]-ω 2 [M]+iω[C]){u(ω)}={P(ω)} (5) Therefore, equation (5) is the harmonic excitation equation with frequency ω, and {u(ω)} is the unit external load displacement response vector of the structure. According to equation (5), with unit simple harmonic load, frequency sweep calculation is performed using the complete method or modal method, and the harmonic response displacement {u(ω)} of each node at each frequency is obtained by finite element software. Step 3: Obtain the element stiffness matrix and nodal displacements under external loads based on the external load coefficients, as detailed below: The element nodal forces of the actual load are: {F e (ω)}=[K e ][λ]{u(ω)}=[K e ]{u e (oh)} (6) In the formula [K e ] is the element stiffness matrix, {u e (ω)} is the displacement matrix of the corresponding element, [λ] is the external load coefficient matrix, that is, the multiple matrix of the actual load to the unit load, {F e (ω)} represents the nodal force matrix. The element stiffness matrix and nodal displacements under external loads are obtained based on the external load coefficient. These are multiplied to obtain the nodal forces at the weld toe or weld root section, and then the moments are derived. The nodal forces and moments of adjacent elements are combined to obtain the nodal forces {F} of the node in its local coordinate system. i (ω)} and nodal torque response {M i (ω)}; Step 4: Calculate the harmonic response structural stress and equivalent structural stress of the structure. Use Miner's linear damage accumulation theory and the master SN curve to obtain the fatigue life of the structural welds, as detailed below: 4-1: Calculate the structural stress and equivalent structural stress of the structure. The structural stress is calculated by transforming the nodal force coordinates and calculating the membrane stress and bending stress, as shown in formulas (7) and (8): In the above formula, σ s (ω), σ m (ω), σ b (ω), F iy (ω) are the harmonic response vectors of structural stress, membrane stress, bending stress, and nodal force in the direction perpendicular to the weld toe line on the mid-thickness surface of the plate, respectively. ix (ω) is the bending moment harmonic response vector along the weld toe line on the thick surface of the weld plate, τ s (ω), τ m (ω), τ b (ω), F ix (ω) are the harmonic response vectors of shear structural stress, shear membrane stress, shear bending stress, and shear nodal force along the weld toe direction on the mid-thickness surface of the plate, respectively. iy (ω) is the bending moment harmonic response vector of the weld plate in the direction perpendicular to the weld toe line, t is the plate thickness, and L is the distance matrix between nodes in the weld thickness section in the structural stress method. Define the response load ratio correction factor: Under load control conditions, it is equation (11); under displacement control conditions, it is equation (12): r = r s (ω) or r = r τ (ω) (12) Let r be a dimensionless function of the bending ratio r under harmonic load; The equivalent structural stress at each node at each frequency is obtained, as shown in formulas (14) and (15): In the above formula, △S s (ω) represents the range of equivalent structural stress variation in the harmonic response perpendicular to the weld toe on the neutral plane of the weld thickness, ΔS. τ (ω) represents the range of equivalent structural stress variation along the weld toe line on the thick surface of the weld plate, where m is a constant; I(r s (ω)), I(r) τ (ω)) refers to the dimensionless function of the bending ratio r of the stress load of the simple harmonic structure and the stress load of the simple harmonic shear structure, respectively, which is obtained by substituting (13) into (11) and (12); Thus, the equivalent structural stress vector can be obtained through equations (14) and (15), that is, the equivalent structural stress amplitude and phase of the weld toe node at frequency ω can be obtained. When △S τ (ω)>△S s (ω) / 3 otherwise △S e (ω)=△S s (oh) (16) β is a constant representing the ratio of fatigue strength between the normal stress based on fatigue testing and the shear stress based on testing. △S e (ω) represents the range of equivalent structural stress variation in the nodal harmonic response; 4-2: Fatigue life of structural welds under simple harmonic vibration is obtained using Miner's linear damage accumulation theory and the master SN curve: The harmonic response of each node is equivalent to the structural stress ΔS. e (ω) forms a response spectrum, if the range of the equivalent structural stress of the i-th order (i=1,2…k) is ΔS ei The number of iterations is n i , Substituting the response spectrum into the calculation formula yields the fatigue life cycle count for this level of failure: N i =(△S ei / C d ) 1 / h (17) In the formula: C d and h are the experimental constants of the structural stress method, N i For △S ei The number of fatigue life cycles of the lower welded joint; The fatigue life of this weld can be predicted, and the cumulative fatigue damage ratio is:

2. The method for predicting the structural stress fatigue life of a welded structure according to claim 1, characterized in that: In step 4-1, m is a constant of 3.

6.

3. The method for predicting the structural stress fatigue life of a welded structure according to claim 1, characterized in that: In step 4-2, if statistical fatigue response spectral density is required, the numerical square of the displacement response spectrum is further converted into a density spectrum, and the S-value is statistically analyzed using the NarrowBand, Sterinberg, Dirlik, or Lalananne methods. e (ω) Density spectrum fatigue.

Images