A structural performance-oriented three-dimensional pipeline support optimization design method

Abstract

The application discloses a three-dimensional pipeline support optimization design method facing structural performance, adopts a moving asymptote method to establish a three-dimensional pipeline support layout optimization design method facing structural performance, adopts a pipe unit and a spring unit to simulate a pipeline and a support to carry out pipeline overall three-dimensional modeling, determines an initial layout support position according to an actual pipeline, solves structural displacement response by using a finite element equation, and builds a pipeline support layout optimization design framework based on the above analysis, takes the number of pipeline support structures as an optimization target, uses structural displacement as an optimization constraint to carry out a penalty function method optimization, and guarantees reasonable support position layout while reducing the number of support structures. The application considers the problem that the number and position of pipeline support structures are difficult to be cooperatively optimized, has a strong applicable range, and solves the problem that the number and position of support layout are difficult to be cooperatively optimized.

Description

Technical Field

[0001] This invention belongs to the field of marine shipbuilding and design, and specifically relates to a three-dimensional pipeline support optimization design method oriented towards structural performance. Background Technology

[0002] Piping systems, as a crucial component of ships, are widely used in their internal structures. For example, the main propulsion system relies on fuel lines to deliver energy to the engine, lubricating oil lines ensure the lubrication and cooling of mechanical components, and cooling water lines maintain the temperature balance of thermal equipment. During navigation, the hull is subject to rocking from waves. To prevent pipe displacement and thus ensure the normal operation of the overall system, its support structure must be rationally laid out to achieve stability and transmit vibrations to the hull. Therefore, the support layout of the piping structure needs to be optimized to meet actual service requirements and achieve a lightweight design for the overall piping structure.

[0003] Regarding the optimization design of pipeline supports, existing research has focused on optimizing pipeline structures using particle swarm optimization and genetic algorithms. The optimization objective is to avoid the engine rotor excitation frequency, with the support layout as the optimization variable. This determines the optimal placement of one or two support structures, thereby ensuring the pipeline structure meets the frequency avoidance design requirements. While this approach yields good frequency avoidance optimization results, these two optimization methods do not consider how to meet structural performance requirements with the minimum number of supports when multiple supports are involved. Under such conditions, these methods cannot meet the design requirements, necessitating new design solutions. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a three-dimensional pipeline support optimization design method oriented towards structural performance, aiming to achieve coordinated optimization of the quantity and location of supports in the layout. The technical solution adopted is as follows: A three-dimensional pipeline support optimization design method oriented towards structural performance is presented below: S1: Based on the actual pipeline structure, a three-dimensional finite element model of the pipeline is established. Pipe elements are used to simulate the main body of the pipeline, and spring elements are used to simulate the support.

[0005] Determine the initial support nodes for the pipeline, and arrange spring units on the nodes to form the initial support layout for the pipeline.

[0006] S2: Based on the pipeline finite element model established in step S1, assemble the total stiffness matrix, apply boundary conditions and loads, and perform finite element analysis to obtain the structural displacement response.

[0007] S3: Calculate the number of spring elements and the displacement with respect to the design variable, spring element density, respectively. x The resolution sensitivity.

[0008] S4: Construct a three-dimensional pipeline support layout optimization formula. After constructing the optimization formula, use the moving asymptote method to solve the optimization problem and update the design variables until convergence, and finally obtain the optimal pipeline support structure layout optimization result.

[0009] S5: Reconstruct the model based on the optimization results obtained in step S4, perform strength verification on the optimization results, and verify that the three-dimensional pipeline optimization results meet the structural design requirements.

[0010] The aforementioned three-dimensional pipeline support optimization design method oriented towards structural performance is further improved by using the penalty function method to process the stiffness matrix of the spring element in step S2, which is expressed as follows: (1) Where: K0 is the spring element stiffness matrix before penalty, K se Let x be the stiffness matrix of the spring element after penalty. i Let the density be the density of the i-th spring element. p As a penalty factor; The spring element stiffness matrix obtained from equation (1) and the derived pipe element stiffness matrix are assembled to obtain the total stiffness matrix of the pipeline structure. Based on this, boundary conditions and loads are applied to perform finite element analysis of the pipeline structure according to the actual service conditions of the pipeline. Based on the finite element analysis results, the displacement results of the pipeline structure are extracted.

[0011] Furthermore, in step S3, the total number of spring elements in the aforementioned three-dimensional pipeline support optimization design method oriented towards structural performance is expressed as follows: (2) Where: M is the total number of springs. n This represents the total number of spring nodes; S3.1: Calculate the analytical sensitivity of the number of spring elements to the design variables, expressed in the following form: (3) S3.2: The analytical sensitivity of the spring element displacement to the design variable is calculated as follows: 1) First, calculate the derivative of the spring element stiffness matrix with respect to the design variables as follows: (4) 2) Use the displacement set of pipeline structure nodes to establish the maximum displacement constraint, expressed in the following form: (5) in This indicates the displacement constraints of the pipeline nodes. Indicates pipeline node j Displacement, This indicates the maximum displacement of the pipeline node. mTo focus on the total number of pipe unit nodes in the displacement region; 3) Differentiate by the chain rule to... The expression is as follows: (6) Then we get The expression is as follows: (7) The linear elastic finite element analysis equation is expressed in the following form: (8) in It is the overall stiffness matrix of the pipeline unit assembly. It is the total stiffness matrix of the spring unit assembly, u is the displacement of the pipeline structure, and F is the total load of the pipeline structure; Can be launched The expression is as follows: (9) According to the chain rule, The expression is as follows: (10) Introducing the adjoint equation to improve the efficiency of sensitivity calculation: (11) in It is the adjoint vector. The analytical sensitivity of pipeline node displacement to design variables can be simplified into the following expression: (12).

[0012] The aforementioned three-dimensional pipeline support optimization design method oriented towards structural performance is further improved by establishing an optimization formula for pipeline support layout in step S4, expressed in the following form: (13) in This is used as a lower bound for design variables.

[0013] This invention addresses the challenge of coordinating the quantity and location of support structures in pipeline layout optimization. It employs a moving asymptote method to establish a three-dimensional pipeline support layout optimization design method oriented towards structural performance. Specifically, pipe elements and spring elements are used to simulate the pipeline and supports for overall three-dimensional modeling. The initial support positions are determined based on the actual pipeline layout. The structural displacement response is solved using finite element equations. Based on this analysis, a pipeline support layout optimization design framework is established. The number of pipeline support structures is used as the optimization objective, and structural displacement is used as the optimization constraint for penalty function optimization. This reduces the number of support structures while ensuring a reasonable support layout. This invention addresses the difficulty of coordinating the quantity and location of pipeline support structures and has a wide range of applications.

[0014] The beneficial effects of this invention are: (1) This invention addresses the problem of poor actual stability of pipelines due to the complex layout of pipeline structures in the hull. It considers the coordinated optimization of the number and location of pipeline supports, constructs a three-dimensional pipeline support layout optimization formula, and uses the moving asymptote optimization method to solve the optimization problem, effectively solving the problem of pipeline support layout optimization design in real service environment.

[0015] (2) This invention significantly reduces the number of pipe supports in the initial support layout, determines the reasonable placement of sufficient support structures, and greatly reduces the number of hull pipe structure supports. This invention is expected to help optimize the three-dimensional pipe support layout in fields such as ship structure design in my country. Attached Figure Description

[0016] Figure 1 A schematic diagram of the initial layout of the spring unit before pipeline structure optimization.

[0017] Figure 2 This is a schematic diagram of the iterative curve of the pipeline structure optimization process.

[0018] Figure 3 This is a schematic diagram of the spring unit layout after the pipeline structure has been optimized.

[0019] Figure 4 This is a flowchart of the three-dimensional pipeline support layout optimization design method of the present invention. Detailed Implementation

[0020] The invention will be further described with reference to the accompanying drawings.

[0021] A three-dimensional pipeline support optimization design method oriented towards structural performance. For example... Figure 4 As shown, the embodiment of the three-dimensional pipeline support layout specifically includes: Step S1: First, based on the geometric characteristics and operating conditions of the actual pipeline system, pipe elements are used to simulate the pipeline structure, and spring elements are used to simulate the support components, thus constructing an initial support layout model for finite element analysis, such as... Figure 1As shown. The specific process includes: establishing a three-dimensional finite element model based on the actual pipeline's routing, cross-sectional dimensions, and material properties. Pipe elements are used to characterize the pipeline's axial and bending stiffness characteristics, while spring elements are used to characterize the elastic constraint effect of the supports. Initial material parameters (such as elastic modulus, Poisson's ratio, density, etc.), structural geometric parameters (such as pipe diameter, wall thickness, support spacing, etc.), and penalty factors are input. p This lays the foundation for subsequent optimization. Then, using the established three-dimensional pipeline finite element model as a reference, the initial candidate support node positions are determined, and spring elements are arranged on these nodes to form the initial support layout scheme.

[0022] Step S2: Based on the three-dimensional pipeline finite element model established in Step 1, assemble the overall structural stiffness matrix. During this process, the penalty function method is used to process the stiffness matrix of the spring elements, as shown in Equation (1), to ensure the physical rationality of the spring elements in the optimization iteration. The stiffness matrix of the spring elements is assembled with the stiffness matrix of the pipe elements to obtain the overall structural stiffness matrix. Appropriate finite element boundary conditions (such as fixed constraints) and external loads are applied according to the actual working conditions. Subsequently, a finite element analysis of the three-dimensional pipeline structure is performed to solve the displacement response of the structure. Based on the analysis results, the calculated displacement data of the pipeline structure nodes are extracted, and the number of spring elements (i.e., supports) in the current layout is counted to provide a basis for subsequent sensitivity calculation and optimization.

[0023] Step S3: Based on the structural displacement response obtained in Step S2 and the current distribution of spring elements, calculate the sensitivity of the number of spring elements to the design variables and the sensitivity of structural displacement to the design variables using equations (2) and (5), respectively. Sensitivity analysis is used to evaluate the influence of each candidate support location on structural performance and is a key step in support layout optimization. Through sensitivity calculation, support locations that contribute significantly to the structural response or are redundant can be identified, thereby guiding the updating of design variables.

[0024] Step S4: Combining the above steps, establish the mathematical formula for the optimization of the three-dimensional pipeline support layout. Using the moving asymptote method, with the number of pipeline support structures as the optimization objective, and structural displacement as the optimization constraint, perform penalty function optimization. Update the design variables in each iteration until the convergence criterion is met. Figure 2 As shown. Finally, the optimal pipeline support structure layout result is output, as shown. Figure 3 As shown in the figure. This embodiment can significantly improve the support efficiency of the pipeline system, reduce manufacturing costs, and ensure safety and reliability under complex operating conditions.

Claims

1. A three-dimensional pipeline support optimization design method oriented towards structural performance, characterized in that, The specific design method is as follows: S1: Based on the actual pipeline structure, a three-dimensional finite element model of the pipeline is established, using pipe elements to simulate the main body of the pipeline and spring elements to simulate the support; Determine the initial support nodes for the pipeline, and arrange spring units on the nodes to form the initial support layout for the pipeline; S2: Based on the pipeline finite element model established in step S1, assemble the total stiffness matrix, apply boundary conditions and loads, and perform finite element analysis to obtain the structural displacement response. S3: Calculate the number of spring elements and the displacement with respect to the design variable, spring element density, respectively. x The analytical sensitivity; S4: Construct a three-dimensional pipeline support layout optimization formula. After constructing the optimization formula, use the moving asymptote method to solve the optimization problem and update the design variables until convergence, and finally obtain the optimal pipeline support structure layout optimization result. S5: Reconstruct the model based on the optimization results obtained in step S4, perform strength verification on the optimization results, and verify that the three-dimensional pipeline optimization results meet the structural design requirements.

2. The three-dimensional pipeline support optimization design method oriented towards structural performance as described in claim 1, characterized in that, In step S2, the penalty function method is used to process the stiffness matrix of the spring element, which is expressed in the following form: (1) Where: K0 is the spring element stiffness matrix before penalty, K se Let x be the stiffness matrix of the spring element after penalty. i Let the density be the density of the i-th spring element. p As a penalty factor; The spring element stiffness matrix obtained from equation (1) and the derived pipe element stiffness matrix are assembled to obtain the total stiffness matrix of the pipeline structure. Based on this, boundary conditions and loads are applied to perform finite element analysis of the pipeline structure according to the actual service conditions of the pipeline. Based on the finite element analysis results, the displacement results of the pipeline structure are extracted.

3. The three-dimensional pipeline support optimization design method oriented towards structural performance as described in claim 1, characterized in that, In step S3, the total number of spring units is expressed as follows: (2) Where: M is the total number of springs. n This represents the total number of spring nodes; S3.1: Calculate the analytical sensitivity of the number of spring elements to the design variables, expressed in the following form: (3) S3.2: The analytical sensitivity of the spring element displacement to the design variable is calculated as follows: 1) First, calculate the derivative of the spring element stiffness matrix with respect to the design variables as follows: (4) 2) Use the displacement set of pipeline structure nodes to establish the maximum displacement constraint, expressed in the following form: (5) in This indicates the displacement constraints of the pipeline nodes. Indicates pipeline node j Displacement, This indicates the maximum displacement of the pipeline node. m To focus on the total number of pipe unit nodes in the displacement region; 3) Differentiate by the chain rule to... The expression is as follows: (6) Then we get The expression is as follows: (7) The linear elastic finite element analysis equation is expressed in the following form: (8) in It is the overall stiffness matrix of the pipeline unit assembly. It is the total stiffness matrix of the spring unit assembly, u is the displacement of the pipeline structure, and F is the total load of the pipeline structure; Can be launched The expression is as follows: (9) According to the chain rule, The expression is as follows: (10) Introducing the adjoint equation to improve the efficiency of sensitivity calculation: (11) in It is the adjoint vector. The analytical sensitivity of pipeline node displacement to design variables can be simplified into the following expression: (12)。 4. A three-dimensional pipeline support optimization design method oriented towards structural performance as described in claim 2 or 3, characterized in that, In step S4, an optimized formula for the pipeline support layout is established, expressed in the following form: (13) in This is used as a lower bound for design variables.

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