A dynamic structural stress calculation method for fatigue life of a welded structure

Abstract

The application discloses a dynamic structural stress calculation method for fatigue life of a welded structure, and comprises the following steps: firstly, a finite element model of a key component is established, boundary element and node subset of a local model of a weld seam of the key component are selected, a flexible body is calculated and obtained by using an improved Craig-Bampton modal synthesis method, the weld seam boundary element and the node subset are defined, and modal node force of the boundary subset is output; based on a modal superposition principle, dynamic node force time history of the local boundary subset of the weld seam is obtained by superimposing model boundary modal node force and modal coordinates of the weld seam of the key component; the model of the weld seam is refined, a weld seam detail is established, and the local model is refined, the number and position of nodes at the boundary are kept corresponding to the boundary subset, stress variation range and cycle number of the dynamic structural stress are calculated by using a rain flow technique, and corresponding equivalent structural stress variation range is calculated based on an ASME standard formula.

Description

Technical Field

[0001] This invention belongs to the field of fully automated products and relates to a dynamic structural stress calculation method for the fatigue life of welded structures. Background Technology

[0002] Existing methods for calculating dynamic structural stress and fatigue assessment techniques for welded structures include the following three types:

[0003] 1) Nominal stress method: Extract the nominal stress at a certain distance from the weld to evaluate the fatigue life of the welded structure. The specific application can be based on the quasi-static method and dynamic calculation results. Then, select the nominal stress SN curves of the structural type and load mode corresponding to the analyzed welded structure from standards such as IIW, BS7608, and JIS to conduct fatigue evaluation [1-4].

[0004] 2) Quasi-static structural stress method: The quasi-static structural stress method is mainly based on the static calculation results of the structure under unit load, calculating the corresponding structural stress. It assumes that there is a linear relationship between load and stress, and converts the static structural stress into dynamic structural stress based on dynamic load data. The fatigue of the weld is then evaluated using rainflow technology and SN curves. [5-8] .

[0005] 3) Modal structural stress method: This method first establishes a finite element model with weld details, calculates and extracts some low-order modes, then transforms the dynamic equation into modal coordinates, calculates and solves the dynamic equation to obtain modal coordinates, calculates the modal structural stress at the weld toe, and obtains the structural stress time history by superimposing the structural stress and modal coordinates. After rainflow counting, the main SN curve can be used to evaluate the fatigue life of the weld [9].

[0006] The types of welded structures that the nominal stress method relies on are limited. In many cases, it is impossible to find welded joint types and stress directions that are consistent with the engineering structure. Therefore, the evaluation results will vary from person to person and are not unique.

[0007] The quasi-static structural stress method neglects the vibration response of the structure and cannot consider the influence of the load frequency on the modal vibration of the structure and the fatigue life of the weld. When the excitation frequency of the external load is much lower than the third-order modal frequency of the structure, good results can be obtained; however, when the external load excitation is close to or overlaps with the modal frequency of the structure, there is a nonlinear relationship between the load amplitude and stress, and the quasi-static evaluation results will have a large deviation.

[0008] Although the modal structural stress method can take into account the influence of structural vibration, it only extracts a portion of the low-order modes. Low-order mode shapes generally describe the overall deformation of the structure. However, the deformation of the local geometry of the weld belongs to the high-frequency mode shape. Even if weld details are established in the model, the low-order modes after the high-order modes are truncated cannot simulate the local deformation of the weld well. Therefore, the calculation of the local stress of the weld will have a certain error. Summary of the Invention

[0009] To address the aforementioned problems, this invention provides a technical solution that primarily aims to resolve difficulties such as the ineffective simulation of local stress concentration in flexible weld seams in rigid-flexible coupling dynamic simulation models, low calculation accuracy, and complex flexible body modeling. The solution includes a dynamic structural stress calculation method for the fatigue life of welded structures, comprising the following steps:

[0010] S1: First, establish the finite element model of the key component, select the boundary elements and node subset of the local model of the weld of the key component, use the improved Craig-Bampton modal synthesis method to calculate the flexible body, define the weld boundary elements and node subset and output the modal node forces of the boundary subset;

[0011] S2: Establish a rigid-flexible coupling dynamic model, apply relevant loads to perform dynamic simulation calculations, and output the time history of the flexible body modal coordinates;

[0012] S3: Based on the principle of modal superposition, the dynamic nodal force time history of a local boundary subset of the weld is obtained by superimposing the modal nodal forces and modal coordinates of the model boundary of a certain weld of a key component.

[0013] S4: Refine the model of a certain weld, establish weld details and refine the local model, and retain the correspondence between the number and position of nodes at the boundary and the boundary subset.

[0014] S5: Apply the dynamic nodal forces of the boundary subset to the refined weld mode, and use a combination of static degree of freedom condensation and inertial release to calculate the deformation and nodal forces of the weld sub-model.

[0015] S6: Based on the structural stress method calculation formula, the structural stress at the corresponding weld toe is calculated for each moment, thereby obtaining the change of dynamic structural stress over time.

[0016] S7: The dynamic structural stress is statistically analyzed using rainflow technology to determine the stress variation range and cycle number, and the corresponding equivalent structural stress variation range is calculated based on the ASME standard formula.

[0017] Furthermore: The process of calculating the flexible body using the improved Craig-Bampton modal synthesis method, defining the weld boundary elements and node subsets, and outputting the modal nodal forces of the boundary subsets is as follows:

[0018] To superimpose the nodal forces corresponding to each mode, the nodal forces of the same node need to be superimposed to form the modal boundary nodal force set [F]. In addition, before assembling the nodal forces, the nodal forces of different elements to the same node need to be summed.

[0019]

[0020] Where: f xmn Let f represent the nodal force in the x-direction of node n in the m-th mode. Each node contains nodal forces in six degrees of freedom directions, i.e., f. x f y f z Forces in three translational directions and m x m y m z The torques in the three rotational directions, and the total number of elements in the aggregated nodal force matrix = the number of boundary nodes n × 6 × the number of modes m. If there are multiple elements in the weld boundary element set that exert nodal forces on the same node, then the nodal forces need to be merged in global coordinates first.

[0021] Furthermore, the process of establishing the rigid-flexible coupling dynamic model is as follows:

[0022] The rigid-flexible coupling dynamic model is composed of a flexible body file connected to the rigid body of the system. The number of modal coordinates is consistent with the number of modal coordinates selected in the definition of the flexible body. The flexible body and the rigid body are connected to the multi-rigid-body system through the constraint equations at the interface of the flexible body. The constraint conditions are introduced into the system equations using the Lagrange multiplier method. By combining the system equations with the multi-rigid-body system equations, the dynamic equations of the rigid-flexible coupling system can be obtained.

[0023]

[0024] In equation (2), Ψ(ξ,t) is the constraint equation; ξ is the generalized coordinate, including displacement coordinate X, Euler angle coordinate ω, and modal coordinate q; Q is the generalized force including the force; L is the Lagrangian function; λ is an undetermined factor; F is the dissipation function of the following form. The dynamic equation is solved using the Newmark integral method to obtain the time history q of the flexible body modal coordinates. i (t), (i = 0, 1, ..., m).

[0025] Furthermore: the expression for the dynamic nodal force time history of the local boundary subset of the weld obtained by superimposing the boundary modal nodal forces and modal coordinates of a certain weld seam model of a key component is as follows:

[0026]

[0027] Where: q i (t) represents the time history of the i-th order flexible body modal coordinates. Let f be the modal coordinate vector. b (t)} 6n×1 The force vector at the boundary node of the sub-model changes over time.

[0028] Furthermore: refine the model of a certain weld, establish weld details and refine the local model, and retain the correspondence between the number and position of nodes at the boundary and the boundary subset;

[0029] S5: The dynamic nodal forces of the boundary subset are applied to the refined weld mode. The displacement and nodal forces of all nodes in the weld sub-model are calculated by combining static degree-of-freedom condensation and inertial release. The process is as follows:

[0030] The stiffness matrix of the weld sub-model corresponds to the internal degrees of freedom u. i and boundary degrees of freedom u b The block representation is as follows:

[0031] (4)

[0032] Among them, f b (t) represents the calculated boundary load. Since the weld sub-model is not subject to external loads, the relationship between the internal degrees of freedom and the boundary degrees of freedom is derived from the first equation (4) as follows:

[0033] {u i (t)}=-[K ii ] -1 [K ib ]{u b (t)} (5)

[0034] Let the transformation matrix [Z] = -[K] ii ] -1 [K ib The acceleration of the internal degrees of freedom of the weld local sub-model can be obtained through equation (6):

[0035]

[0036] The mass matrix of a weld seam model for a critical component is divided into boundary degrees of freedom and internal degrees of freedom, and written in block matrix form as follows:

[0037] (7)

[0038] Based on the static degree-of-freedom condensation method, the mass matrix can be condensed onto the boundary degrees of freedom using the following equation (8). Solving equation (9) yields the acceleration on the boundary degrees of freedom, which, when multiplied by the transformation matrix [Z], provides the internal acceleration.

[0039]

[0040]

[0041]

[0042] The model load vector {F(t)} of a certain weld of the key component is superimposed on the right side of equation (4) to form the overall load vector of the weld sub-model. Theoretically, the acceleration load and the external load of the weld sub-model are in equilibrium, and the weld sub-model is in force equilibrium. One node (with the smallest acceleration) is selected as the support point, that is, displacement constraints are applied to the 6 degrees of freedom of the node, so that all displacement vectors {u} in (4) can be solved. i (t)} and {u b (t)}, where the displacement vector corresponding to the node associated with element e is {u e (t)}.

[0043] The deformation of the weld sub-model and the nodal forces and moments at the weld toe can be obtained by following the above process for each moment, thus obtaining the change of nodal forces over time.

[0044]

[0045] The nodal forces of adjacent elements are merged, and the nodal forces and moments are sorted according to the weld line to obtain the nodal force and moment sequences {F(t)} and {M(t)} distributed along the weld line. Based on the nodal load and the distance l between adjacent nodes, the equivalent nodal load is calculated using the length equivalence matrix L (Equation 12). The nodal forces and moments corresponding to the weld line nodes are transformed into line loads {f(t)} and line moments {m(t)} on the edge of the element in that direction.

[0046] (12)

[0047]

[0048] Furthermore, the process of statistically analyzing the stress variation range and cycle number of the dynamic structure stress using rainflow technology is as follows:

[0049] Based on the structural stress method calculation formula, the structural stress at each moment is calculated, and rainflow counting is performed on the structural stress time history to obtain the stress variation range. and the number of cycles;

[0050]

[0051] Where: {σ m (t)} represents the membrane stress, {σ m f(t)} represents the bending stress, d represents the plate thickness, and f(t) and m(t) represent the weld line force and line moment, respectively.

[0052] The process of statistically analyzing the stress variation range and cycle number of dynamic structures using rainflow technology is as follows:

[0053] The equivalent structural stress variation range is calculated for each stress cycle using the formulas provided in the ASME standard.

[0054]

[0055] In the formula, I(r) is a dimensionless function of the bending ratio r (r = Δσ). b / Δσ s ), m = 3.6, d is the plate thickness.

[0056] Furthermore, fatigue damage and life of the weld were calculated using the master SN curve, based on the stress variation range of different structural grades. and the corresponding number of loops n i Combining Miner's linear damage accumulation, the lifespan calculation formula can be obtained as follows:

[0057]

[0058] Equation (16) is the formula for calculating the vibration fatigue life of welded structures under time-domain load based on the master SN curve, where C d h is a parameter related to the main SN curve.

[0059] The present invention provides a dynamic structural stress calculation and fatigue assessment technology for welded structures. (1) This technology is based on rigid-flexible coupling dynamic simulation and can be applied to the working state simulation and weld fatigue assessment of large and complex mechanical systems.

[0060] (2) It can combine the structural stress method with dynamic simulation by measuring strain, and realize the vibration fatigue life assessment of welded structures;

[0061] (3) The use of local sub-model technology for weld seams effectively reduces the degree of freedom of the dynamic model, while also being able to better simulate the impact of local deformation and stress concentration of weld seams on fatigue life.

[0062] Therefore, the dynamic structural stress acquisition technology proposed in this invention can reduce the size and computational load of the flexible body model, while improving the calculation accuracy of local deformation and stress of the weld, thus compensating for the impact of high-frequency truncation processing of the modal superposition method on the fitting accuracy of local deformation of the weld.

[0063] The main application areas of this method are: (1) This method can realize the dynamic structural stress and fatigue assessment of welds based on the dynamic simulation results of rigid-flexible coupling of rail vehicles; (2) This method can support the dynamic structural stress recovery of welds without the establishment of a detailed weld model; (3) Combined with the detailed explanation of rigid-flexible coupling simulation, this method can be applied to the fatigue assessment of welds under complex working load conditions of engineering machinery structures; (4) This method can also be applied to the fatigue assessment of welds under dynamic loads of welded structures in other industries, such as aviation, automobiles, ships and other fields, as well as the comparison and verification of improvement schemes.

[0064] This invention improves the accuracy of calculating local stress in welds using existing rigid-flexible coupling dynamic simulation methods for fatigue calculation of welded structures, simplifies the complexity of the dynamic model, and facilitates comparison of different schemes.

[0065] The technology has the following advantages: 1) The method of selecting the local model of the weld of key components is adopted by the technology, which avoids the problem of the decrease in fitting accuracy of local deformation of weld in the high-frequency mode stage of the modal superposition method, makes up for the shortcomings of the modal superposition method, and can effectively improve the calculation accuracy of dynamic structural stress.

[0066] 2) By adopting the method of selecting the local model of the weld of key components, the flexible body does not need to build a detailed model of the weld, which can effectively simplify the difficulty of rigid-flexible coupling dynamic modeling and improve simulation efficiency.

[0067] 3) This method can be directly applied to the simulation results of rigid-flexible coupling previously done. Only the weld and model need to be refined. There is no need to modify the model or repeat the calculation, which makes it convenient to compare and analyze with previous work.

[0068] 4) Since the local weld model and the rigid-flexible coupling model of the selected key components have a certain degree of independence, the local structure of the weld can be easily optimized without repeatedly modifying the rigid-flexible coupling and simulation, making the scheme comparison and analysis faster.

[0069] 5) This method combines rigid-flexible coupling simulation with sub-model technology to realize the simulation of the working state of complex mechanical systems and the assessment of weld fatigue life, and has a wide range of applications. Attached Figure Description

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1This is a schematic diagram of the decomposition of a flexible body finite element model;

[0072] Figure 2 This is a schematic diagram of the nodal forces of the boundary element;

[0073] Figure 3 This is a detailed schematic diagram of the weld seam sub-model. Detailed Implementation

[0074] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0077] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0078] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0079] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0080] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0081] A method for calculating the dynamic structural stress of a welded structure fatigue life includes the following steps:

[0082] S1: First, establish the finite element model of the key component, select the boundary elements and node subset of the local model of the weld of the key component, use the improved Craig-Bampton modal synthesis method to calculate the flexible body, define the weld boundary elements and node subset and output the modal node forces of the boundary subset;

[0083] A critical component refers to a part within a mechanical system that is important and thus subject to fatigue analysis. A weld local model is a detailed finite element mesh model of the local geometric features of a weld line within this component.

[0084] S2: Establish a rigid-flexible coupling dynamic model, apply relevant loads to perform dynamic simulation calculations, and output the time history of the flexible body modal coordinates;

[0085] S3: Based on the principle of modal superposition, the dynamic nodal force time history of a subset of the local boundary of a weld seam is obtained by superimposing the boundary modal nodal forces and modal coordinates of a model (also known as a sub-model) of a certain weld seam in a key component; the model of a certain weld seam in a key component is a fine modeling of the local geometric features of a weld line inside the key component using finite element mesh.

[0086] S4: Refine the model of a certain weld, establish weld details and refine the local model, and retain the correspondence between the number and position of nodes at the boundary and the boundary subset.

[0087] S5: Apply the dynamic nodal forces of the boundary subset to the refined weld mode, and use a combination of static degree of freedom condensation and inertial release to calculate the deformation and nodal forces of the weld sub-model.

[0088] S6: Based on the structural stress method calculation formula, the structural stress at the corresponding weld toe is calculated for each moment, thereby obtaining the change of dynamic structural stress over time.

[0089] S7: The dynamic structural stress is statistically analyzed using rainflow technology to determine the stress variation range and cycle number, and the corresponding equivalent structural stress variation range is calculated based on the ASME standard formula.

[0090] Steps S1 / S2 / S3 / S4 / S5 / S6 / S7 are executed sequentially;

[0091] The corresponding flexible finite element model is established for the structural component to be analyzed as shown above. Figure 1 Without creating weld details, large mesh structures can be used for discretization. The interface between a conventional flexible body and an external rigid body can be defined, such as... Figure 1 As shown, it is also necessary to define the local boundary elements and node sets of the weld, as follows: Figure 1 The red cells represent the boundary cell set, and the white nodes represent the boundary node set.

[0092] The process of calculating the flexible body using the improved Craig-Bampton modal synthesis method, defining weld boundary elements and node subsets, and outputting the modal nodal forces of the boundary subsets is as follows:

[0093] The nodal forces corresponding to each mode are assembled in the order of the boundary node subsets to form a point force geometry matrix [F]. Furthermore, before assembling the nodal forces, the nodal forces of different elements at the same node need to be summed. For example... Figure 2 As shown;

[0094]

[0095] Where: f xmnThis represents the nodal force in the x-direction of node n in the m-th mode. Each node contains nodal forces in six degrees of freedom directions, f. 11 This represents the nodal force of element 1 on node 1. The nodal force includes forces in six degrees of freedom, i.e., f. x f y f z Forces in three translational directions and m x m y m z Torque in three directions of rotation, f 11 The first number represents the cell number, and the second array represents the node number; f 12 and f 22 The nodal forces belonging to node 2 need to be synthesized from the nodal forces in each of the 6 degrees of freedom directions. The total number of force elements in the set = the number of boundary nodes n × 6 × the number of modes m.

[0096] Furthermore, the process of establishing the rigid-flexible coupling dynamic model is as follows:

[0097] The rigid-flexible coupling dynamic model is constructed by connecting the flexible body file with the rigid body of the system. Actual working loads are applied, and dynamic simulation calculations are performed. The number of modal coordinates is consistent with the number of modal coordinates selected in the definition of the flexible body. The flexible vehicle body and the rigid body are connected to the multi-rigid-body system through constraint equations at the interface of the flexible body. The constraint conditions are introduced into the system equations using the Lagrange multiplier method. By simultaneously solving the equations of the flexible-flexible coupling system with those of the multi-rigid-body system, the dynamic equations of the rigid-flexible coupling system can be obtained.

[0098]

[0099] In equation (2), Ψ(ξ,t) is the constraint equation; ξ is the generalized coordinate, including displacement coordinate X, Euler angle coordinate ω, and modal coordinate q; Q is the generalized force including the force; L is the Lagrangian function; λ is an undetermined factor; F is the dissipation function of the following form. The dynamic equation is solved using the Newmark integral method to obtain the time history q of the flexible body modal coordinates. i (t), (i = 0, 1, ..., m). This process can be performed using the commercial software ADAMS.

[0100] Furthermore, the expression for the dynamic nodal force time history of the local boundary subset of the weld obtained by superimposing the boundary modal nodal forces and modal coordinates of a certain weld seam model of a key component is as follows: The time history of the boundary nodal load is obtained by superimposing the set of modal boundary nodal forces and modal coordinates, i.e. Figure 1 The nodal forces at the white nodes shown in the diagram change over time (loads on each node with 6 degrees of freedom), where t represents time:

[0101]

[0102] Where: q i (t) represents the time history of the i-th order flexible body modal coordinates. Let f be the modal coordinate vector. b (t)} 6n×1 The change of the force vector at the boundary nodes of the sub-model over time;

[0103] Furthermore: S4: Refine the model of a certain weld seam ( Figure 1 (Yellow section) Establish weld details and refine the local model, considering the local geometric details of the weld as follows: Figure 2 The refined weld local model shown retains the correspondence between the number and position of nodes at the boundary and the boundary subset; due to the small mass of the weld local model, inertial forces are ignored, and the sub-model basically maintains a state of force equilibrium.

[0104] S5: Apply the dynamic nodal forces of the boundary subset to the refined weld mode. Using a combination of static degree-of-freedom condensation and inertial release methods, calculate the deformation and nodal forces of the weld sub-model. For each moment of the boundary external load, calculate the nodal forces at the weld toe using a combination of static degree-of-freedom condensation and inertial release methods (e.g., ...). Figure 3 The yellow portion represents the weld toe node. The process of how the nodal force at the weld toe of the weld structure changes over time is as follows:

[0105] The stiffness matrix of a certain weld seam model corresponds to the internal degrees of freedom u. i and boundary degrees of freedom u b The block representation is as follows:

[0106] (4)

[0107] Where f(t) is the calculated boundary load. Since the weld sub-model is not subject to external loads, the relationship between the internal degrees of freedom and the boundary degrees of freedom is derived from the first equation of equation (4) as follows:

[0108] {u i (t)}=-[K ii ] -1 [K ib ]{u b (t)} (5)

[0109] Let the transformation matrix [Z] = -[K] ii ] -1 [K ib ], obtain the acceleration relationship between the internal degrees of freedom and the boundary degrees of freedom:

[0110]

[0111] The degrees of freedom of the local sub-model of the weld are divided into boundary degrees of freedom and internal degrees of freedom, which can be written in block matrix form as follows:

[0112] (7)

[0113] Based on the static degree-of-freedom condensation method, the mass matrix can be condensed onto the boundary degrees of freedom using the following equation (8). Solving equation (9) yields the acceleration on the boundary degrees of freedom, and multiplying it by the transformation matrix gives the internal acceleration.

[0114]

[0115]

[0116]

[0117] The inertial load vector {F(t)} of a certain weld of a key component is superimposed on the right side of equation (4) to form the overall load vector of the weld sub-model. The deformation of the weld sub-model and the nodal force at the weld toe are obtained by using the inertial release method. The change of nodal force with time can be obtained for each moment by following the above process.

[0118] Furthermore, the process of statistically analyzing the stress variation range and cycle number of the dynamic structure stress using rainflow technology is as follows:

[0119] Based on the structural stress method calculation formula, the structural stress at each moment is calculated, and rainflow counting is performed on the structural stress time history to obtain the stress variation range. and the number of cycles;

[0120]

[0121] Where: {σ m (t)} represents the membrane stress, {σ m f(t)} represents the bending stress, d represents the plate thickness, and f(t) and m(t) represent the weld line force and line moment, respectively.

[0122] Furthermore: Based on the formulas provided in the ASME standard, the equivalent structural stress variation range is calculated for each stress cycle.

[0123]

[0124] In the formula, I(r) is a dimensionless function of the bending ratio r (r = Δσ). b / Δσ s ), m = 3.6, d is the plate thickness.

[0125] The fatigue assessment technique based on the dynamic structural stress calculation method for the fatigue life of welded structures uses the master S-N curve to calculate the fatigue damage and life of the weld, based on the stress variation range of different grades of equal structures. and the corresponding number of loops n i Combining Miner's linear damage accumulation, the lifespan calculation formula can be obtained as follows:

[0126]

[0127] Equation (13) is the formula for calculating the vibration fatigue life of welded structures under time-domain load based on the master SN curve, where C d h is a parameter related to the main SN curve.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

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[0137] [9]. Fang Ji, Zhao Wenzhong, Pu Mingwei. Research on fatigue life prediction method of welded structure based on modal superposition method [J]. Vibration and Shock, 2015, 35(5):187-192.

Claims

1. A method for calculating the dynamic structural stress of a welded structure's fatigue life, characterized in that: Includes the following steps: S1: First, establish the finite element model of the key component, select the boundary elements and node subset of the local model of the weld of the key component, use the improved Craig-Bampton modal synthesis method to calculate the flexible body, define the weld boundary elements and node subset and output the modal node forces of the boundary subset; S2: Establish a rigid-flexible coupling dynamic model, apply relevant loads to perform dynamic simulation calculations, and output the time history of the flexible body modal coordinates; S3: Based on the principle of modal superposition, the dynamic nodal force time history of a local boundary subset of the weld is obtained by superimposing the modal nodal forces and modal coordinates of the model boundary of a certain weld of a key component. S4: Refine the model of a certain weld, establish weld details and obtain a refined local model, so that the number and position of nodes at the boundary correspond one-to-one with the boundary subset; S5: Apply the dynamic nodal forces of the boundary subset to the refined weld mode, and use a combination of static degree of freedom condensation and inertial release to calculate the displacement and nodal forces of the weld sub-model. S6: Based on the structural stress method calculation formula, the structural stress at the corresponding weld toe is calculated for each moment, thereby obtaining the change of dynamic structural stress over time. S7: The dynamic structural stress is statistically analyzed using rainflow technology to determine the stress variation range and cycle number, and the corresponding equivalent structural stress variation range is calculated based on the ASME standard formula. S4: Refine the model of a certain weld, establish weld details and obtain a refined local model, so that the number and position of nodes at the boundary correspond one-to-one with the boundary subset; S5: The dynamic nodal forces of the boundary subset are applied to the refined weld mode. The displacement and nodal forces of all nodes in the weld sub-model are calculated by combining static degree-of-freedom condensation and inertial release. The process is as follows: The stiffness matrix of the weld sub-model corresponds to the internal degrees of freedom u. i and boundary degrees of freedom u b The block representation is as follows: （4） Among them, f ｂ (t) represents the calculated boundary load. Since the weld sub-model is not subject to external loads, the relationship between the internal degrees of freedom and the boundary degrees of freedom is derived from the first equation (4) as follows: （5） Let the transformation matrix The acceleration of the internal degrees of freedom of the weld sub-model is obtained by equation (6): （6） The mass matrix of a weld seam model for a critical component is divided into boundary degrees of freedom and internal degrees of freedom, and written in block matrix form as follows: （7） Based on the static degree-of-freedom condensation method, the mass matrix is ​​condensed onto the boundary degrees of freedom using the following equation (8). Solving equation (9) yields the acceleration on the boundary degrees of freedom, and multiplying it by the transformation matrix [Z] yields the internal acceleration. : （8） （9） （10） The model load vector of a certain weld of a key component Superimposed on the right side of equation (4), the overall load vector of the weld sub-model is formed. Theoretically, the acceleration load and the external load of the weld sub-model are in equilibrium, and the weld sub-model is in force equilibrium. Select the node with the smallest acceleration as the support point, that is, apply displacement constraints on the 6 degrees of freedom of this node, and then solve for all displacement vectors {u} in (4). i (t)} and {u b (t)}, where the displacement vector corresponding to the node associated with element e is { }; By following the above procedure at each moment, the change of nodal force over time can be obtained: （11） Where: k represents a matrix, which merges the nodal forces of adjacent elements and sorts the nodal forces and moments along the weld line to obtain the sequence of nodal forces and moments distributed along the weld line. and Based on node load and distance between adjacent nodes Using length equivalent matrix Calculate the equivalent load at the nodes, converting the nodal forces and moments corresponding to the weld nodes into line loads on the element edges in that direction. and linear moment ; （12） (13)。 2. The dynamic structural stress calculation method for fatigue life of welded structures according to claim 1, characterized in that: The process of calculating the flexible body using the improved Craig-Bampton modal synthesis method, defining weld boundary elements and node subsets, and outputting the modal nodal forces of the boundary subsets is as follows: To superimpose the nodal forces corresponding to each mode, the nodal forces of the same node need to be superimposed to form the modal boundary nodal force set [F]. In addition, before assembling the nodal forces, the nodal forces of different elements to the same node need to be summed. （1） Where: f xmn Let f represent the nodal force in the x-direction of node n in the m-th mode. Each node contains nodal forces in six degrees of freedom directions, i.e., f. x f y f z Forces in three translational directions and m x m y m z The torques in the three rotational directions, the total number of elements in the nodal force matrix after aggregation = the number of boundary nodes n × 6 × the number of modes m. If multiple elements in the weld boundary element set exert nodal forces on the same node, then the nodal forces need to be merged in the global coordinate system first.

3. The dynamic structural stress calculation method for fatigue life of welded structures according to claim 1, characterized in that: The process of establishing the rigid-flexible coupling dynamic model is as follows: The rigid-flexible coupling dynamic model is composed of a flexible body file connected to the rigid body of the system. The number of modal coordinates is consistent with the number of modal coordinates selected in the definition of the flexible body. The flexible body and the rigid body are connected to the multi-rigid-body system through the constraint equations at the interface of the flexible body. The constraint conditions are introduced into the system equations using the Lagrange multiplier method. The dynamic equations of the rigid-flexible coupling system are obtained by solving the equations of the flexible body and the multi-rigid-body system simultaneously. （2） In equation (2), These are the constraint equations; Generalized coordinates, including displacement coordinates Euler angle coordinates and modal coordinates ; For the broad sense of power, including influence; It is a Lagrange function; Undetermined factors; The dynamic equations are solved using the Newmark integration method to obtain the time history of the flexible body's modal coordinates, given the dissipation function of the following form. , i=0,1,…m, where m is the number of modes.

4. The dynamic structural stress calculation method for fatigue life of welded structures according to claim 2, characterized in that: The expression for the dynamic nodal force time history of the local boundary subset of the weld obtained by superimposing the boundary modal nodal forces and modal coordinates of a model of a certain weld seam of a key component is as follows: （3） in: Represents the time history of the i-th order flexible body modal coordinates. For modal coordinate vectors, The force vector at the boundary node of the sub-model changes over time.

5. The dynamic structural stress calculation method for fatigue life of welded structures according to claim 1, characterized in that: The process of statistically analyzing the stress variation range and cycle number of dynamic structures using rainflow technology is as follows: Based on the structural stress method calculation formula shown in Equation (14), the structural stress at each moment is calculated, and rainflow counting is performed on the structural stress time history to obtain the stress variation range. and the number of cycles; （14） in: For membrane stress, Let d be the bending stress, d be the plate thickness, and f(t) and m(t) be the weld line force and line moment, respectively.

6. The dynamic structural stress calculation method for fatigue life of welded structures according to claim 5, characterized in that: The equivalent structural stress variation range is calculated based on the ASME standard formula: (15) In the formula, I (r) is the bending ratio r dimensionless function, r = σ b / σ s , m =3.6, d The thickness is the plate thickness.

7. The dynamic structural stress calculation method for fatigue life of welded structures according to claim 6, characterized in that: The fatigue damage and life of the weld were calculated using the master SN curve, based on the stress variation range of different structural grades. and the corresponding number of loops Combining Miner's linear damage accumulation, the lifespan calculation formula can be obtained as follows: (16) Equation (16) is the formula for calculating the vibration fatigue life of welded structures under time-domain load based on the master SN curve, where C d , h These are the parameters related to the main SN curve.

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