A Small Deformation Contact Nonlinear Simulation Method

Abstract

This invention discloses a small-deformation contact nonlinear simulation method, belonging to the field of contact nonlinear simulation technology, including the following steps: S1, using friction springs at the contact interface for contact simulation; S2, setting nonlinear analysis conditions in finite element analysis software; S3, performing small-deformation contact nonlinear simulation and calculation on the structure. This invention, employing the above-mentioned small-deformation contact nonlinear simulation method, provides important reference for the accurate calculation and design of modular units, beam placement, tunnel lining, and other structures, saving materials, reducing energy consumption, and improving production efficiency. Its application can be embedded into programs to form automated options, realizing digital twins.

Description

Technical Field

[0001] This invention relates to the field of contact nonlinear simulation technology, and in particular to a method for simulating small-deformation contact nonlinearity. Background Technology

[0002] In existing technologies, when beams are placed on the ground, and when prefabricated components such as tunnel linings and modular modular houses are assembled, the connections involve different interfaces, and these interfaces may separate or slide. In finite element simulations, hinged or rigid joints are often used to handle these boundary conditions, such as in simulations of structure-ground contact, lining connections, and modular unit contact. Traditional contact simulations often establish contact relationships between nodes on the structural surface and their projection points on the corresponding contact interfaces. As contact separates or slides, each point on the structural surface needs to find a corresponding node on the contact interface. When contact separates or slides, the points on the structural surface need to re-establish contact relationships with points 1-7 on the corresponding contact interfaces as they move, such as... Figure 15 As shown, this results in a large computational load and requires a dense mesh at the corresponding contact interface; otherwise, points on the structural surface may not correspond to the corresponding contact interface. The corresponding contact interface must also be continuous. However, the actual working condition of the interface connection is between hinged and rigid, exhibiting a semi-rigid effect. This causes the calculation results to deviate from the actual situation, affecting the calculation accuracy and leading to a significant gap between the designed performance of the structure and its actual service conditions. This results in material waste or potential safety hazards. Therefore, it is necessary to simulate the actual boundary conditions of the structure to accurately evaluate its mechanical properties. Summary of the Invention

[0003] The purpose of this invention is to provide a small deformation contact nonlinear simulation method, which provides an important reference for the accurate calculation and design of structures such as modular units, beam placement, and tunnel lining, saving materials, reducing energy consumption, and improving production efficiency. Its application can be embedded into programs to form automated options and realize digital twins.

[0004] To achieve the above objectives, the present invention provides a method for simulating small deformation contact nonlinearity, comprising the following steps:

[0005] S1. A friction spring is used at the contact interface to simulate contact.

[0006] S2. Set up nonlinear analysis conditions in the finite element analysis software;

[0007] S3. Perform small deformation contact nonlinear simulation and calculation on the structure.

[0008] Preferably, a friction spring is used in S1 for simulation, allowing disengagement in the normal direction and sliding in the tangential direction of the contact interface.

[0009] Preferably, the normal setting of the contact interface in S1 includes the following three cases: the structure is in contact with the ground; the structure is in contact with each other; and the contact interface normal is detached.

[0010] Preferably, when the structure is in contact with the ground, the normal stiffness of the contact interface is taken as the vertical stiffness of the spring per unit area of ​​10. 6 kN / mm / m 2 When structures are in contact, the normal stiffness of the contact interface is determined based on the elastic modulus of the material and the measured value. When the contact interface is normally separated, the normal stiffness is reduced based on the structural material and the measured value. After the contact interface begins to separate, the normal stiffness of the contact interface is taken as the reduced stiffness.

[0011] Preferably, the tangential setting of the contact interface in S1 includes: when the structure is in contact with the ground or between structures, the tangential stiffness between the contact interfaces is small and needs to be determined based on the friction coefficient and measured values; when the contact interface slides tangentially, the tangential stiffness decreases and is reduced based on the structural material and measured values; after the contact interface starts to slide, the tangential stiffness of the contact interface is the reduced stiffness.

[0012] Preferably, in S2, since the contact interface allows for separation and sliding, nonlinear analysis needs to be considered. Since the deformation at the contact interface is small, the stiffness of the structure cannot be re-formed based on the deformation of the structure, i.e., geometric nonlinearity is not considered.

[0013] Therefore, the present invention employs the aforementioned small deformation contact nonlinear simulation method, which provides an important reference for the accurate calculation and design of modular units, beam placement, tunnel lining and other structures, saving materials, reducing energy consumption and improving production efficiency. Its application can be embedded into programs to form automated options and realize digital twins.

[0014] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1 This is a model diagram of an I-beam using a small deformation contact nonlinear simulation method according to the present invention;

[0016] Figure 2 This is a model diagram of the contact position between the I-beam and the support using Damper-Friction Spring connection elements, which is a small deformation contact nonlinear simulation method of the present invention.

[0017] Figure 3 This is a deformation model diagram of the contact position between an I-beam and a support, based on a small deformation contact nonlinear simulation method of the present invention.

[0018] Figure 4This invention provides a small deformation contact nonlinearity simulation method that does not consider geometric nonlinearity when describing the axial force diagram of the connecting element.

[0019] Figure 5 This invention provides a small deformation contact nonlinear simulation method that considers the axial force diagram of the connecting element when considering large deformation.

[0020] Figure 6 This invention provides a small deformation contact nonlinear simulation method using Damper-Friction Spring connection elements, showing the axial force diagram of the connection elements.

[0021] Figure 7 This invention provides a small deformation contact nonlinear simulation method using linear connection elements, and the axial force diagram of the connection element is shown.

[0022] Figure 8 This invention provides a small deformation contact nonlinear simulation method using a fixed support, and the resulting diagram shows the support reaction force.

[0023] Figure 9 This is a diagram showing the deformation of a small deformation contact nonlinear simulation method of the present invention when using Damper-Friction Spring connection elements;

[0024] Figure 10 This is a deformation diagram of a small deformation contact nonlinear simulation method of the present invention when using linear connection units;

[0025] Figure 11 This is a diagram showing the deformation of a small deformation contact nonlinear simulation method of the present invention when a fixed support is used;

[0026] Figure 12 This is a stress diagram of a small deformation contact nonlinear simulation method of the present invention using Damper-Friction Spring connection elements;

[0027] Figure 13 This is a stress diagram of a small deformation contact nonlinear simulation method of the present invention using linear connection elements;

[0028] Figure 14 This is a stress diagram of a small deformation contact nonlinear simulation method of the present invention using a fixed support;

[0029] Figure 15 This is a diagram of a traditional contact simulation method, which is a small deformation contact nonlinear simulation method according to the present invention. Detailed Implementation

[0030] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0032] Example 1

[0033] This invention provides a method for simulating small deformation contact nonlinearity, comprising the following steps:

[0034] S1. A friction spring is used at the contact interface to simulate contact.

[0035] Friction springs are used for simulation. The contact interface is allowed to disengage in the normal direction and slide in the tangential direction. The initial displacement is set as a nonlinear condition to simulate the nonlinearity of small deformation contact.

[0036] The normal settings of the contact interface include the following three cases: contact between the structure and the ground; contact between structures; and separation of the contact interface normals.

[0037] When the structure is in contact with the ground, the normal stiffness of the contact interface is very large. It is recommended to take the vertical stiffness of the spring per unit area as 10. 6 kN / mm / m 2 This achieves the theoretical effect. When structures are in contact, the normal stiffness of the contact interface is relatively small, and its value is determined based on the elastic modulus of the material and measured values. Since the normal of the contact interface can detach, the normal stiffness will inevitably decrease after detachment. When the normal of the contact interface detaches, the normal stiffness needs to be reduced based on the structural material and measured values. After the contact interface begins to detach, the normal stiffness of the contact interface is taken as the reduced stiffness.

[0038] The tangential setting of the contact interface includes: when the structure is in contact with the ground or between structures, the tangential stiffness between the contact interfaces is relatively small and needs to be determined based on the friction coefficient and measured values; since the tangential direction of the contact interface allows sliding, the tangential stiffness will inevitably decrease after sliding. When the contact interface slides tangentially, the tangential stiffness decreases. The tangential stiffness is reduced according to the structural material and measured values. After the contact interface starts to slide, the tangential stiffness of the contact interface is taken as the reduced stiffness.

[0039] S2. Set up nonlinear analysis conditions in the finite element analysis software;

[0040] Since the contact interface allows for detachment and sliding, nonlinear analysis needs to be considered. Since the deformation is small, it is neither necessary nor possible to regenerate the stiffness of the structure based on the deformation, i.e., geometric nonlinearity is not considered.

[0041] S3. Perform small deformation contact nonlinear simulation and calculation on the structure.

[0042] Example 2

[0043] Taking an I-beam as an example, in SAP2000, an I-beam is created and placed on a flat platform, such as... Figure 1 and Figure 2 As shown. The clear distance between the platforms is L=6m, the support length at both ends is 0.5m, the flange width of the I-beam is 300mm, the height is 600mm, the plate thickness is 16mm, the material is Q355 steel, and the uniformly distributed surface load within the clear distance is 100kN / m. 2 Without considering structural weight, a damper-friction spring is used to simulate the friction spring, with a unit spacing of 100mm and a unit length of 50mm.

[0044] Contact connections are achieved using damper-friction springs in the connection unit. In the attribute definition, U1 refers to the normal direction of the contact interface, i.e., the axial direction of the connection unit. U1 stiffness: Due to the non-linearity of the contact between the structure and the foundation surface, linear analysis stiffness is not considered for now. The axial attribute is defined as compression only, not tension. Since this embodiment involves the structure contacting the ground, the vertical stiffness should be sufficiently large, approaching rigidity. For now, the axial stiffness per unit area of ​​the connection unit is taken as 10. 6 kN / mm / m 2 Based on the dependent area of ​​the connecting element, the initial axial stiffness of the connecting element in the nonlinear analysis is calculated.

[0045] The stiffness when the connection is disengaged should be less than the stiffness when at rest. Therefore, the sliding stiffness should be less than the initial stiffness. The value should be determined according to the structural material. For now, we take 1 / 10 of the initial stiffness. The preload displacement is taken as -0.1~-1mm as an initial condition for nonlinear analysis. The termination displacement is the displacement when the connection element starts to take the sliding stiffness. When it is 0, the stiffness is taken as the sliding stiffness by default during calculation.

[0046] U2 and U3 refer to the tangential direction of the contact interface, i.e., the horizontal direction of the connecting unit. U2 and U3 stiffness: the shear position is the location where shear deformation of the connecting unit occurs, i.e., the intersection of the connecting unit and the structure. The horizontal direction is defined as compression, simulating tangential friction. Since the axial resultant force is larger than the horizontal resultant force, the shear stiffness is smaller. Based on engineering experience, the tangential stiffness per unit area of ​​the connecting unit is tentatively taken as 10. 4 kN / mm / m 2 The stiffness during sliding should be less than the stiffness at rest. Therefore, the sliding stiffness should be less than the initial stiffness. The value should be determined according to the structural material. For now, we take 1 / 10 of the initial stiffness. The preload displacement and termination displacement are both set to 0.

[0047] To account for contact nonlinearity, the analysis type should be nonlinear. Since the deformation of general structures generally satisfies the small deformation assumption, large displacement is not selected. However, when considering geometric nonlinearity, especially large deformation, after the contact interface slides, the axial stiffness of the connecting elements remains unchanged, but the normal stiffness of the contact interface decreases significantly, which is inconsistent with the design conditions. Figure 3 As shown, where, Figure 3 In this context, 'a' represents the direction of U1 without considering geometric nonlinearity. Figure 3 In the diagram, 'b' represents the direction of U1 considering geometric nonlinearity. However, this analysis primarily considers contact nonlinearity, neglecting changes in structural geometric stiffness and thus not requiring consideration of the P-Delta effect. Therefore, the final solution is to disregard geometric nonlinearity.

[0048] Due to the complexity of the structure, too many steps in the calculation would lead to excessive computation time without improving accuracy; a balance must be struck between accuracy and efficiency. Verification has shown that in nonlinear analyses similar to small deformation contact, setting the minimum value to 1 ensures both accuracy and minimizes computation time.

[0049] The axial force of the connection element can be reflected by the corresponding support reaction force. The following will demonstrate the accuracy of the Damper-Friction Spring connection element and analysis method settings from the perspectives of support reaction force, deformation, and stress.

[0050] To verify the accuracy of the analysis method settings, keeping other conditions unchanged, the geometric nonlinearity in the load case was set to two modes: one without considering geometric nonlinearity and the other considering large deformation. The support reaction at one end of the beam when geometric nonlinearity is ignored is as follows: Figure 4 As shown, considering the support reaction force at one end of the beam during large deformation, as follows: Figure 5 As shown, due to symmetry, when considering large deformations, the sum of the support reactions is inconsistent with the sum of the external loads, meaning the connecting elements fail prematurely, failing to achieve the actual simulation effect. When geometric nonlinearity is not considered, the sum of the support reactions is consistent with the sum of the external loads; therefore, geometric nonlinearity should not be considered, verifying the accuracy of the analysis method.

[0051] To verify the accuracy of the Damper-Friction Spring connection element simulation, Damper-Friction Spring connection elements, linear connection elements, and fixed supports were used to simulate the contact. The simulation was then conducted by comprehensively comparing the axial force of the connection elements or the reaction force of the supports, the deformation at the contact position, and the stress of the overall structure.

[0052] When using a damper-friction spring to connect elements, the axial force of the connecting elements is as follows: Figure 6 As shown, only the connecting units near the inner side are under compression, while the remaining connecting units are out of service due to tension, which is consistent with the actual situation. The axial force of the connecting units when using linear connecting units is as follows: Figure 7 As shown, the connection unit involves both tension and compression, which does not match the actual situation. The support reaction force when using fixed supports is as follows: Figure 8As shown, F1, F2, and F3 represent the x-direction, y-direction, and z-direction reaction forces of the support in the finite element analysis software, respectively. The z-direction reaction force is the vertical support reaction force. When the structure is fixed to the ground, the vertical reaction force F3 in the support reaction force can be both positive and negative, indicating that there is tension and compression in the vertical direction at the contact position, which is inconsistent with the actual situation.

[0053] When using a damper-friction spring connection unit, the contact point separates at the tension point, and the deformation is consistent with the actual situation. Figure 9 As shown, when using linear connection units and fixed supports, the deformation at the contact positions is similar, and there is no phenomenon of separation or sliding, which is inconsistent with the actual situation. Figure 10 and Figure 11 As shown.

[0054] When using the Damper-Friction Spring connection element, the stress on the upper flange of the I-beam at the support is close to zero, while that on the lower flange is not zero. This difference in stress between the upper and lower flanges indicates that the support is neither fixed nor hinged after using the Damper-Friction Spring connection element. The stress situation is as follows: Figure 12 As shown, when using linear connection elements and fixed supports, the stresses on the upper and lower flanges at the support are not zero and are similar in magnitude. This indicates that the simulated contact between the linear connection elements and the fixed supports does not match the actual situation. The stress conditions are as follows: Figure 13 and Figure 14 As shown.

[0055] Therefore, this invention employs the aforementioned small-deformation contact nonlinear simulation method, providing important reference for the accurate calculation and design of modular elements, beam support, tunnel lining, and other structures, as well as for material saving, energy reduction, and improved production efficiency. Its application can be embedded into programs to form automated options, realizing digital twins. In SAP2000, after using Damper-Friction Spring connection elements, points on the structural surface consistently maintain a contact relationship with a certain point on the contact interface, without any change in the contact relationship. Mesh density is not required, reducing computational load. Furthermore, by not considering nonlinear deformation, the normal stiffness of the contact interface remains unchanged before separation, more closely resembling reality. When the contact interface is a support, multiple points can be used to replace the contact interface and establish a contact relationship with the structural surface.

[0056] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for simulating small deformation contact nonlinearity, characterized in that: Includes the following steps: S1. A friction spring is used to simulate the contact at the contact interface, and the friction spring is simulated by the connecting unit Damper-FrictionSpring. The simulation uses a friction spring, where the contact interface is allowed to disengage in the normal direction and slide in the tangential direction. The normal settings for contact interfaces include the following three cases: contact between structure and ground; contact between structures; The contact interface is detached from the normal direction; When the structure is in contact with the ground, the normal stiffness of the contact interface is taken as the vertical stiffness of the spring per unit area, which is 10. 6 kN / mm / m 2 When structures are in contact, the normal stiffness of the contact interface is determined based on the elastic modulus of the material and the measured value. When the contact interface is normally separated, the normal stiffness is reduced based on the structural material and the measured value. After the contact interface begins to separate, the normal stiffness of the contact interface is the reduced stiffness. The tangential setting of the contact interface includes: when the structure is in contact with the ground or between structures, the tangential stiffness between the contact interfaces is small and needs to be determined based on the friction coefficient and measured values; when the contact interface slides tangentially, the tangential stiffness decreases and is reduced based on the structural material and measured values. After the contact interface starts to slide, the tangential stiffness of the contact interface is taken as the reduced stiffness. S2. Set up nonlinear analysis conditions in the finite element analysis software; Since the contact interface allows for detachment and sliding, nonlinear analysis needs to be considered. Since the deformation at the contact interface is small, the stiffness of the structure cannot be reconstructed based on the deformation of the structure, i.e., geometric nonlinearity is not considered. S3. Perform small deformation contact nonlinear simulation and calculation on the structure.

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