KR101327111B1 - Topology optimization method of linking finite element analysis program and numerical analysis program and design method for ultrasonic transducer using the same - Google Patents

Abstract

The present invention relates to a method for phase optimization linked with a finite-element analysis program and a numerical value analysis program and a method for designing the phase optimization of an ultrasonic transducer by using the same. The present invention performs dynamic feature analysis and the modeling of an analyzed model in the finite-element analysis program and performs design variable update for phase optimization in the numerical value analysis program. Therefore, with the invention, phase optimization is possible even in a field in which the phase optimization is impossible due to a complex initial shape. In addition, the phase optimization is performed by using the numerical value analysis program so that a reasonable phase optimization result is obtained by applying various phase optimization algorithm to even a model with a physically impossible result. [Reference numerals] (S2100) Determining design variable and purpose function of model to be interpreted;(S2200) Modeling model to be interpreted by using finite-element analysis program;(S2300) Interpreting motion feature of model by using finite-element analysis program;(S2400) Transmitting motion feature interpreted in finite-element analysis program to numerical value analysis program;(S2500) Renewing design variable by using phase optimization algorithm of numerical value analysis program;(S2600) Receiving design variable;(S2700) Transmitting renewed design variable of numerical value analysis program to finite-element analysis program;(S2800) End optimization

Description

Topology optimization method of linking finite element analysis program and numerical analysis program and design method for ultrasonic transducer using the same}

The present invention relates to a phase optimization method in which a finite element analysis program and a numerical analysis program are linked, and a method of designing a phase optimization of an ultrasonic transducer using the same. More specifically, modeling and dynamic characteristic analysis of a model to be analyzed are performed in a finite element analysis program. Updating design variables for phase optimization is related to a phase optimization method in which a finite element analysis program and a numerical analysis program performed in a numerical analysis program and a phase optimization design method of an ultrasonic transducer using the same.

Phase optimization is a method of optimizing the model according to the objective function regardless of the initial shape of the model. The objective function of the phase optimization is set for the finite element to be optimized and is accompanied by design constraints to find a reasonable solution. In other words, it is possible to derive the desired solution by setting artificial variables and design constraints for the desired condition and going through a phase optimization algorithm.

Phase optimization can be performed using various programs, for example, a numerical analysis program can be used. Numerical analysis is a mathematical method of numerical approximation. In cases where it is impossible to obtain an accurate solution, the solution can be solved using theory or techniques for control without evaluating the method of calculation and the error associated with numerical calculation. Topology optimization using numerical analysis program is used in various fields such as engineering, physics, economics, etc., and can perform phase optimization even when the physical result is impossible. However, there is a problem that the result value cannot be presented intuitively when performing the phase optimization using a numerical analysis program.

Consider using a computer simulation technique called finite element analysis (FEA) to obtain intuitive results. Finite element analysis is commonly used to determine stresses and displacements in mechanical objects or systems. In engineering, computer modeling is used to set external factors such as physical properties and loads, and to obtain visualized results. When optimizing the phase with the finite element analysis program, the internal section of the model can be seen, so the result of the analysis is intuitive. However, the finite element analysis program is difficult to use immediately for phase optimization because a lot of memory is allocated when the analysis is performed.

Therefore, a phase optimization method capable of performing phase optimization even in a model having a physically impossible result or a model in which an initial model has a complicated shape and intuitively presenting the result is needed.

It is an object of the present invention to apply a phase optimization irrespective of the initial shape of a model to be analyzed, and to obtain a rational phase optimization program even for a model in which the result of the phase optimization is physically impossible. This paper provides a phase optimization method in conjunction with a numerical analysis program and a method for designing a phase optimization method for an ultrasonic transducer using the same.

In order to achieve the above object, the phase optimization method in which the finite element analysis program and the numerical analysis program according to the embodiment of the present invention are implemented in a computer capable of driving the finite element analysis program and the numerical analysis program, Determining design variables, objective functions, modeling the model to be analyzed using the finite element analysis program, analyzing the dynamic characteristics of the model using the finite element analysis program, Transfer the dynamic characteristics to the numerical program and update the design variables using the phase optimization algorithm coded in the numerical program. If the design variables converge, the phase optimization is terminated. If the design variables do not converge, the numerical program is updated. Finite element analysis program for design variables And transmitting the data to the dynamic characteristics of the model and performing the process again.

According to an embodiment of the present invention, a phase optimization method in which a finite element analysis program and a numerical analysis program are linked to each other converts data to be readable by another program when the finite element analysis program and the numerical analysis program transmit data to each other. A virtual buffering unit can be used.

According to an embodiment of the present invention, a method of optimizing a phase by linking a finite element analysis program and a numerical analysis program may be a finite element analysis program, and a numerical analysis program may be a matlab.

The topology optimization method in which the finite element analysis program and the numerical analysis program in accordance with an embodiment of the present invention are implemented in a computer that can run the finite element analysis program and the numerical analysis program. Steps, modeling the model to be analyzed using the finite element analysis program, formulating the model using the finite element analysis program, obtaining differential equations for finite element analysis, eigenvalues according to the differential equations, and each node of the model Analyzing the dynamic characteristics of the model by calculating the displacement, acceleration, velocity, mass, stiffness, damping matrix, and natural frequency of the model, and transmitting the dynamic characteristics of the model analyzed by the finite element analysis program to the numerical analysis program. To update the design variables using the phase optimization algorithm If the system and design variables converge, the phase optimization is terminated. If the design variables do not converge, the numerical analysis program transfers the updated design variables to the finite element analysis program, and then executes the analysis from the dynamic characteristics of the model. .

In the phase optimization method in which the finite element analysis program and the numerical analysis program according to an embodiment of the present invention are used, the updating of the design variable using the phase optimization algorithm coded in the numerical program is performed by tracking the target mode among the vibration modes of the eigenvalues. The method may include: modifying the objective function using the eigenvalue of the target mode, and differentiating the modified objective function into the design variable to obtain a sensitivity and updating the design variable according to the sensitivity. The tracking of the target mode among the vibration modes of the eigenvalues may use Modal Assurance Criterion (MAC).

In the phase optimization method in which the finite element analysis program and the numerical analysis program according to the embodiment of the present invention update the design variable according to the sensitivity, the design variable may be updated using an OC (Optimal Criteria). You can also set volume constraints when updating design variables.

According to an embodiment of the present invention, an ultrasonic transducer phase optimization design method in which a finite element analysis program and a numerical analysis program are linked is implemented in a computer capable of driving a finite element analysis program and a numerical analysis program. Defining the objective function and the target frequency, modeling the transducer using the finite element analysis program, formulating the transducer modeled using the finite element analysis program, and deriving the derivative for finite element analysis. Analyze the dynamic characteristics of the model by obtaining equations, eigenvalues according to differential equations, displacements of each node of the model, acceleration, velocity, mass, stiffness, damping matrix, and natural frequency, and analyzed by finite element analysis program. Transfer the dynamic characteristics of the model to the numerical program Update the design variables using the phase optimization algorithm coded in the numerical analysis program. If the design variables converge, the phase optimization is terminated. If the design variables do not converge, the updated design variables are converted into the finite element analysis program. Transmitting and analyzing the dynamic characteristics of the model.

In the ultrasonic transducer phase optimization design method in which a finite element analysis program and a numerical analysis program are linked according to an embodiment of the present invention, the step of updating a design variable by using a phase optimization algorithm coded in the numerical analysis program is a target among eigen oscillation modes. Tracing the mode, modifying the objective function using the eigenvalue of the target mode, and differentiating the modified objective function into the design variable to obtain a sensitivity and updating the design variable according to the sensitivity. The tracking of the target mode among the vibration modes of the eigenvalues may use Modal Assurance Criterion (MAC).

In the ultrasonic transducer phase optimization design method in which the finite element analysis program and the numerical analysis program according to an embodiment of the present invention are updated, the updating of the design variable according to the sensitivity may be performed by using an OC (Optimal Criteria). . In addition, the volume constraint can be set by setting a retention zone with a density of always one in the body to prevent the volume of the body of the ultrasonic transducer from being updated when the design variable is updated. The preservation area may be at the top and bottom of the center of the body.

The phase optimization method in which the finite element analysis program and the numerical analysis program according to the present invention and the phase optimization design method of the ultrasonic transducer using the same are modeled using the finite element analysis program for various initial shape models. Therefore, the phase optimization is possible even in the field where the phase optimization was impossible. In addition, since the phase optimization is performed using a numerical analysis program, it is possible to obtain reasonable phase optimization results by applying various phase optimization algorithms to a model that results in physically impossible results.

1 is a block diagram illustrating a computer capable of implementing a phase optimization method in which a finite element analysis program and a numerical analysis program according to an embodiment of the present invention are implemented.
2 is a flowchart illustrating a phase optimization method in which a finite element analysis program and a numerical analysis program are linked according to an embodiment of the present invention.
3 is a diagram illustrating the concept of Modal Assurance Criterion (MAC).
4 is a diagram illustrating a concept of updating a design variable by using an OC method.
5 conceptually illustrates the side of an ultrasonic transducer simplified into a cuboid shape.
6 is a diagram illustrating a phase optimization result of an ultrasonic transducer in which a storage area is set.
FIG. 7 is a diagram illustrating an optimized shape according to a phase optimization result of an ultrasonic transducer in which a storage area is set.
8 is a view showing an ultrasonic transducer manufactured in an optimized shape.
9 is a view showing the results of measuring the amplitude of the ultrasonic transducer using a laser vibrometer.
10 is a view showing a safety chamber for the accelerated life test of the ultrasonic transducer.
FIG. 11 is a diagram showing displacement of pressure and non-pressure state of the ultrasonic transducer every 10 hours.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Note that, in the drawings, the same components are denoted by the same reference symbols as possible. Further, the detailed description of known functions and configurations that may obscure the gist of the present invention will be omitted. For the same reason, some of the components in the drawings are exaggerated, omitted, or schematically illustrated.

1 is a block diagram illustrating a computer capable of implementing a phase optimization method in which a finite element analysis program and a numerical analysis program according to an embodiment of the present invention are implemented.

As shown in FIG. 1, the computer 100 according to an embodiment of the present invention includes an input unit 110, a display unit 120, a memory unit 130, and a controller 140. The input unit 110 is used by a user who uses the computer 100 to operate the computer 100. The input unit 110 may be a keyboard, a mouse, or the like. The display unit 120 indicates an operating state of the computer 100. The display unit 120 may be a monitor or the like. The memory unit 130 is used for data storage. The memory unit 130 stores the finite element analysis program and the numerical analysis program. In the present embodiment, the finite element analysis program may be a comsol and the numerical analysis program may be matlab, but is not limited thereto. The controller 140 controls the computer 100 to perform user input. In the present embodiment, the controller 140 controls the finite element analysis program and the numerical analysis program to be driven well, and controls the finite element analysis program and the numerical analysis program to transmit data to each other.

FIG. 2 is a flowchart illustrating a phase optimization method in which a finite element analysis program and a numerical analysis program are linked according to an embodiment of the present invention. FIG. 3 is a diagram illustrating a concept of Modal Assurance Criterion (MAC), and FIG. 4 is an OC (Optimal). The concept of updating a design variable using the Criteria) method is shown.

As shown in FIG. 2, in order to perform a phase optimization by linking a finite element analysis program and a numerical analysis program, first, a design variable and an objective function of a model to be analyzed are determined (s2100). The design parameters depend on the phase optimization method applied. Phase optimization methods include homogenization, density, and levelset methods. Homogenization performs optimization by introducing microstructures in the design domain. Divide the entire design area into a myriad of small unit cells and treat some of each unit cell as empty space. The stiffness of the unit cell is proportional to the rest of the unit cell minus the empty space. And the mechanical stiffness of each structure is calculated by the homogenization method and the optimization model is found. The density method is presented by Rozvany and Zhou and is also called SIMP. The density method considers the density of each element in the finite element model as a design variable and turns the entire problem into a density distribution problem. Once the density distribution is established, the element with a median between 0 and 1 becomes a problem. To solve this problem, penalization of density values is performed. The level set method changes the phase by moving the boundary of the structure, and can clearly express the boundary between the material and non-material regions. Another method, evolutionary structural optimization, mimics the evolution of ecosystem organisms and eliminates inefficient factors in proportion to element stress and von Mises stress. The objective function may be a function of frequency maximization or a function of frequency shift.

When the design variable and the objective function are determined, the model to be analyzed is modeled using the finite element analysis program (S2200). Modeling is the creation of three-dimensional shapes in the virtual space inside the computer. Generally, finite element analysis programs provide various modeling methods.

When the modeling is completed, the dynamic characteristics of the model are analyzed using the finite element analysis program (S2300). To analyze the dynamic characteristics of the model, model the modeled model. Formalization means to find differential equations for finite element analysis. The differential equation is used to find the eigenvalue, displacement of each node of the model, acceleration, velocity, mass, stiffness, damping matrix, and natural frequency.

Since the principle of analyzing the dynamic characteristics of the model in the finite element analysis program is already known, a detailed description thereof will be omitted, and only the eigenvalues will be briefly described below. Eigenvalue Problems Basically, partial differential equations are used to perform the analysis. The partial differential equation is

는 고유치의 linearization point이다. 첫번째 식의 우항 f는 source term으로 모델의 경계값에 의하여 결정된다. 수학식 1을 일반적인 형태로 쓰면 수학식 2와 같은 형태로 표현할 수 있다.
In Equation (1)

Is the linearization point of the eigenvalue. The right side f of the first equation is the source term, determined by the model's bounds. If Equation 1 is used in a general form, it may be expressed as Equation 2.

는 외부 가진을 뜻한다. U는 모델의 변위를 뜻하며, E, D, K, N은 솔루션 벡터 U를 계산하기 위하여 이용한다. 만약 E=0이라면 모델은 선형 고유치 문제가 되며 0이 아닌 경우에는 이차 고유치 문제로 표현한다. 비선형 고유치 문제를 풀기 위해서 유한요소해석 프로그램에서는 이차식을 선형으로 근사하여 식을 다시 유도한다. 그 이후 수학식 2는

로 간략히 표현할 수 있다.In Equation 2 E is the mass matrix, D is the damping matrix, K is the stiffness matrix means if N _F and

Means externally excited. U is the displacement of the model, and E, D, K, N are used to calculate the solution vector U. If E = 0, then the model is a linear eigenvalue problem. In order to solve the nonlinear eigenvalue problem, the finite element analysis program derives the equation by linearly approximating the quadratic equation. After that, Equation 2 is

Can be briefly expressed as:

주위에 선형 근사식의 series로 고유값을 계산한다.Problems in calculating eigenvalues sometimes arise when boundary conditions or material properties include nonlinear functions. This case can be treated as a series of quadratic eigenvalue problems. The finite element analysis program has an eigenvalue linearization point

Compute the eigenvalues as a series of linear approximations around it.

When the eigenvalue problem is expressed as the case of the natural frequency problem, the relationship between the eigenvalue and the natural frequency is expressed by Equation 3.

The eigenvectors resulting from the eigenvalue problem represent the mode shape of the model. If there is a damping value in the model, the eigenfrequency is derived from the damped eigenvalue, and the eigenvalue is expressed as an imaginary number. The real value of the substituted natural frequency is the natural frequency value of the real model, and the imaginary part represents the damping value. In natural frequency analysis, the scale of the model's eigenmodes is randomly determined by the solver.

Through this series of processes, the finite element analysis program can calculate the displacement and acceleration velocity of each degree of freedom of each node, and find the mass, stiffness, damping matrix, and eigenvector eigenfrequency.

 When the dynamic characteristics of the model are analyzed, the calculated dynamic characteristics are transmitted to the numerical analysis program (S2400). In the present embodiment, when the finite element analysis program and the numerical analysis program transmit data between each other, the data transmitted using the virtual buffering unit may be converted to be readable by another program.

When the numerical analysis program receives the dynamic characteristics of the model, the design variable is updated using a coded phase optimization algorithm (S2500). To update the design variables, the target mode is first tracked among the eigenvalue vibration modes. Solving the differential equations for the finite element model yields a plurality of eigenvalues. In this case, the target mode to be optimized is tracked among vibration modes of each eigenvalue. Modal Assurance Criterion (MAC) may be used to track the target mode. MAC is calculated as shown in Equation 4, and the concept is as shown in FIG.

는 최적화 대상이 되는 사인 진동 모드를 나타내는 벡터이며,

는 최적화 진행 중인 모델의 현재 진동 모드를 나타내는 벡터이다. 고유치들의 진동 모드의 고유 벡터와 MAC을 계산하여 1에 근접한 가장 높은 값이 나온 고유치의 진동 모드가 타겟 모드가 된다. In Equation 4,

Is a vector representing the sine vibration mode to be optimized.

Is a vector representing the current vibration mode of the model under optimization. The target mode is the vibration mode of the eigenvalues, which calculates the eigenvectors and MACs of the vibration modes of the eigenvalues and obtains the highest value close to one.

Once the target mode is found, the objective function is modified using the eigenvalues of the target mode. After modifying the objective function, the sensitivity is obtained and the design variables are updated according to the sensitivity. Sensitivity is obtained by differentiating the objective function with the design variables. The methods for improving design variables in the phase optimization method include an OC (Optimal Criteria) method and a Method of Moving Asymptotes (MMA) method. The application of the OC method to the static problem is shown in Equation 5.

은 설계밀도 값의 최대 변화 한계이며

는 수치적인 감쇠 값이다.

는 수학식 6과 같이 주어진다.

Is the maximum change limit of the design density value

Is the numerical attenuation value.

Is given by Equation 6.

는 목적 함수이며,

의 분자항은 민감도 값을 의미한다. 분모의 λ는 라그랑지안 승수로써 위상최적화 코드 안에서 bi-sectioning 알고리즘을 통해 구한다. In Equation (6)

Is the objective function,

The molecular term of means the sensitivity value. The λ of the denominator is the Lagrangian multiplier, obtained from the bi-sectioning algorithm in the phase optimization code.

를 동적 문제에 맞게 수정한 형태는 수학식 7과 같다. OC 방법을 이용하여 설계 변수를 갱신하는 개념은 도 4에 도시되어 있다.
Equation 5 is the application of the OC method for the static problem and if it is for the dynamic problem, it should be slightly modified because the sensitivity value for the dynamic problem may have a negative value.

Is modified to fit the dynamic problem as shown in Equation (7). The concept of updating design variables using the OC method is illustrated in FIG. 4.

When the design variable is updated, it is determined whether the updated design variable converges (S2600). If the design variables do not converge (No), the updated design variables are transmitted to the finite element analysis program (S2700). The finite element analysis program repeats from the analysis of the dynamic characteristics of the model using the updated design variables. If the design variables converge (Yes), the optimization ends and an optimized model is derived.

Example

According to an embodiment of the present invention, a phase optimization method in which a finite element analysis program and a numerical analysis program are combined is applied to the design of an ultrasonic transducer. Transducers are one of the important components for delivering ultrasonic energy to semiconductors in semiconductor bonding equipment. Successful ultrasonic bonding requires longitudinal natural frequencies of ultrasonic equipment. Until now, however, ultrasonic transducers have been designed using engineer experience and trial and error methods. Since this method is not suitable for the rapidly changing field of semiconductor packaging technology, phase optimization has been applied to the design of ultrasonic transducers.

In the present embodiment, the finite element analysis program used Comsol, and the numerical analysis program used Matlab. The shape of the ultrasonic transducer is simplified to a cuboid shape having a body portion with a square side, as shown in FIG. The design variable is the finite element density of the ultrasonic transducer body part and the objective function is a function that changes the natural frequency of the longitudinal mode of the body part. Specifically, the objective function is to minimize the difference between the natural frequency and the target frequency in the longitudinal mode of the initial model while maintaining the mode.

The SIMP method was used to formulate the phase optimization, and the density was updated using the OC method. The MAC method is used to track the target longitudinal vibration mode. After the optimization, we compared the shape of the 2D and 3D models. To determine the mechanical properties and validity of the design, we fabricated a 3D model and measured the vibration displacement using a laser vibrometer and performed an accelerated life test of 1500 hours.

During the phase optimization, the density of each element has a value between 0 and 1 to update mass and stiffness. If the element's density is zero, it is the absence of material. On the other hand, if the element has a density of 1, that is where the material is. While phase optimization is repeatedly calculated, Young's modulus and density are approximated by the interpolation function as shown in Equation (8).

The interpolation function has an exponential form as shown in Equation 9.

The equation of the objective function is shown in Equation 10. In Equation 10, ω _i means the natural frequency of the model during iteration calculation and ω _t means the target frequency.

0.7 was used in this example as the f volume limit condition in the objective function. X _min prevents sigular metrics. In this embodiment, it is set to 0.001.

In order to obtain the sensitivity, in this embodiment, the objective function is differentiated into the design variable, and the sensitivity function is expressed by Equation (11).

The sensitivity function converted into the matrix form is shown in Equation 12.

And converting the sensitivity function into the form of strain energy and kinetic energy is shown in Equation 13.

In Equation 13, Estrain and Ekinetic represent strain energy and kinetic energy, respectively. The function represented in the form of energy as shown in Equation 13 has an advantage. For example, it is an extensibility applicable to various FEM codes.

MAC is used to track the longitudinal sine waveform during the phase optimization calculation. In this example, weighted MAC is used. WMAC is a modified MAC method that provides weighting functions using density in preparation for physically impossible behavior of low density elements. WMAC is calculated as in Equation 14.

In this embodiment, the OC method was used to update the design variable based on the sensitivity value. The OC method is an algorithm that raises or lowers the design variables of elements based on sensitivity values. The OC method has been described in equations (5) and (6).

In order to prevent the body volume of the ultrasonic transducer from becoming zero during the optimization process, a volume constraint must be set. In this embodiment, a fixed region in which the density does not change during the optimization process is set. As shown in Fig. 5, the storage area was the upper and lower portions of the center of the body portion. This is because a general ultrasonic transducer is formed at the upper and lower portions of the center of the body portion. In this example, the conservation zones were set to two sizes and optimized for each. In the following description, a model having a length of 8 mm in the conservation area is called PF8 and a model PF16 having a length of 16 mm in the conservation area. The result of optimizing the PF8 using the SIMP method is as shown in FIG. 6 (a), and the optimization shape is as shown in FIG. 7 (a). The result of optimizing the PF16 using the SIMP method is as shown in FIG. 6B, and the optimization shape is as shown in FIG. 7B.

To verify the validity of the design, two transducer models were fabricated with the resulting shape. The model was made with sus by wire cutting. An ultrasonic transducer manufactured with an optimized shape for PF8 is shown in FIG. 8A, and a transducer manufactured with an optimized shape for PF16 is shown in FIG. 8B.

In order to operate the ultrasonic transducer, an ultrasonic generator was applied to the ultrasonic transducer with 60 kHz ultrasonic waves corresponding to 1 kV. The amplitude of the excited ultrasonic transducer was measured using a laser vibrometer. Measurements were made at the end point (EP) and bonding point (BP) of the ultrasonic transducer. The measurement result is as shown in FIG. The difference between the natural frequencies of the optimized model obtained using a computer and the natural frequencies of the model actually produced was measured to be less than 1%.

In addition, an experiment was conducted on an acceleration environment corresponding to 1500 hours of the ultrasonic transducer (PF16). For the accelerated life test, a safety chamber as shown in FIG. 10 was constructed and repeatedly excited with a constant pressure of 2 MPa.

FIG. 11 is a diagram showing displacement of pressure and non-pressure state of the ultrasonic transducer every 10 hours. All of the optimized ultrasonic transducers showed robust behavior even after the end of life test.

It should be noted that the embodiments of the present invention disclosed in the present specification and drawings are only illustrative of the present invention in order to facilitate description of the present invention and to facilitate understanding of the present invention and are not intended to limit the scope of the present invention. It will be apparent to those skilled in the art that other modifications based on the technical idea of the present invention are possible in addition to the embodiments disclosed herein.

100: computer 110: input unit
120: display unit 130: memory unit
140:

Claims (14)

A phase optimization method implemented in a computer that can run a finite element analysis program and a numerical analysis program,
Determining a design variable and an objective function of the model to be analyzed;
Modeling the model to be analyzed using the finite element analysis program;
Analyzing dynamic characteristics of the model using the finite element analysis program;
Transmitting the dynamic characteristics of the model analyzed by the finite element analysis program to the numerical analysis program, and updating the design variable using a phase optimization algorithm coded in the numerical analysis program; And
If the design variable converges, the phase optimization is terminated. If the design variable does not converge, the updated design variable is transferred from the numerical analysis program to the finite element analysis program, and the process is performed again from the step of analyzing dynamic characteristics of the model. And a phase optimization method in which the finite element analysis program and the numerical analysis program are linked to each other. The method of claim 1,
When the finite element analysis program and the numerical analysis program transmit data to each other, a finite element analysis program and a numerical analysis program comprising a virtual buffering unit converting the transmitted data to be readable by another program. Linked phase optimization method. The method of claim 1,
The finite element analysis program is a comsol, and the numerical analysis program is a matlab. The phase optimization method in which the finite element analysis program and the numerical analysis program are linked. A phase optimization method implemented in a computer that can run a finite element analysis program and a numerical analysis program,
Determining a design variable and an objective function of the model to be analyzed;
Modeling the model to be analyzed using the finite element analysis program;
The model is formulated using the finite element analysis program to obtain differential equations for finite element analysis, eigenvalues according to the differential equation, displacement of each node of the model, acceleration, velocity, mass, stiffness, and damping matrix. Analyzing the dynamic characteristics of the model by obtaining a natural frequency;
Transmitting the dynamic characteristics of the model analyzed by the finite element analysis program to the numerical analysis program;
Updating the design variable using a phase optimization algorithm coded in the numerical analysis program; And
If the design variable converges, the phase optimization is terminated. If the design variable does not converge, the updated design variable is transferred from the numerical analysis program to the finite element analysis program, and the process is performed again from the step of analyzing dynamic characteristics of the model. And a phase optimization method in which the finite element analysis program and the numerical analysis program are linked to each other. 5. The method of claim 4,
The step of updating a design variable by using a phase optimization algorithm coded in the numerical analysis program,
Tracking a target mode among the vibration modes of the eigenvalues;
Modifying the objective function using the eigenvalues of the target mode; And
Obtaining a sensitivity by differentiating the modified objective function into the design variable and updating the design variable using an OC (Optimal Criteria) according to the sensitivity; and a finite element analysis program and a numerical analysis program comprising: Phase optimization method in conjunction with. The method of claim 5,
Tracking the target mode among the vibration mode of the eigenvalue,
A phase optimization method in which a finite element analysis program and a numerical analysis program are linked using a Modal Assurance Criterion (MAC). delete The method of claim 5,
The updating of the design variable according to the sensitivity may include:
A phase optimization method incorporating a finite element analysis program and a numerical analysis program characterized by setting volume constraints. In the ultrasonic transducer phase optimization design method having a body using a computer capable of driving a finite element analysis program and a numerical analysis program,
Determining a design function of the transducer as a finite element density of the body portion, and determining an objective function and a target frequency;
Modeling the transducer using the finite element analysis program;
Formulate the modeled transducer using the finite element analysis program to obtain differential equations for finite element analysis, eigenvalues according to the differential equations, displacement of each node of the model, acceleration, velocity, mass, stiffness Analyzing a dynamic characteristic of the model by obtaining a damping matrix and a natural frequency;
Transmitting the dynamic characteristics of the model analyzed by the finite element analysis program to the numerical analysis program;
Updating the design variable using a phase optimization algorithm coded in the numerical analysis program; And
If the design variable converges, the phase optimization is terminated. If the design variable does not converge, the updated design variable is transferred from the numerical analysis program to the finite element analysis program, and the process is performed again from the step of analyzing dynamic characteristics of the model. Ultrasonic transducer phase optimization design method comprising the step of linking the finite element analysis program and the numerical analysis program. 10. The method of claim 9,
The step of updating a design variable by using a phase optimization algorithm coded in the numerical analysis program,
Tracking a target mode among the vibration modes of the eigenvalues;
Modifying the objective function using the eigenvalues of the target mode; And
Obtaining a sensitivity by differentiating the modified objective function into the design variable and updating the design variable using an OC (Optimal Criteria) according to the sensitivity; and a finite element analysis program and a numerical analysis program comprising: Ultrasonic Transducer Phase Optimization Design Method The method of claim 10,
Tracking the target mode among the vibration mode of the eigenvalue,
Ultrasonic transducer phase optimization design method incorporating finite element analysis program and numerical analysis program using Modal Assurance Criterion (MAC). delete The method of claim 10,
Ultrasonic transducer phase optimization design method in conjunction with a finite element analysis program and a numerical analysis program, characterized in that for setting the preservation area does not change the density in the body portion to prevent the volume of the body portion of the ultrasonic transducer to zero. The method of claim 13,
The preservation area is the ultrasonic transducer phase optimization design method in conjunction with the finite element analysis program and the numerical analysis program, characterized in that the upper and lower portions of the center of the body.

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