JP2016076154A - Analyzer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique capable of highly accurately analyzing vibration energy.SOLUTION: A first calculation unit attaches a condition to a model divided into finite number elements with joints as demarcations, and calculates a displacement vector, a velocity vector, an acceleration vector, an elastic force vector, a damping force vector and an inertial force vector as values to be calculated for a joint of each element. A second calculation unit calculates a joint force vector at a certain joint from the values calculated for a plurality of elements adjacent to the joint. A third calculation unit calculates a vibration energy vector from the joint force vector and the velocity vector. A display section displays the calculated joint force vector and vibration energy vector. The second calculation unit calculate a joint elastic force vector E at a certain joint by adding together only positive components of elastic force vectors E1 to E4 calculated for the respective elements adjacent to the joint for a component projected in the direction of the displacement vector u of the joint.SELECTED DRAWING: Figure 2

Description

  The present invention relates to an analysis apparatus, and more particularly to an apparatus for analyzing vibration of a structure by a finite element method.

  As a technique for analyzing the vibration of the structure, there is an analysis technique using a finite element method. For example, by calculating the displacement of each element and the internal force acting on each element for a model composed of a plurality of elements, a transfer vector representing vibration energy transmitted in the element is derived (for example, Patent Literature 1).

JP 2007-298324 A

  In the vibration analysis of a structure, it is desirable that components caused by elastic force, damping force, and inertial force can be derived individually.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide a technique capable of accurately analyzing vibration energy transmitted through a structure.

  In order to solve the above-described problem, an analysis apparatus according to an aspect of the present invention adds a condition to a model divided into a finite number of elements having a node as a boundary, and calculates a displacement as a value calculated for the node for each element. A first force calculation unit for calculating a vector, a velocity vector, an acceleration vector, an elastic force vector, a damping force vector, and an inertial force vector, and a value calculated for each of a plurality of elements adjacent to a certain node. Calculating the magnitude of vibration energy by the inner product of the nodal force vector and the velocity vector, and calculating the vector direction of the vibration energy from the gradient of the magnitude of vibration energy between adjacent nodes. A third calculation unit that calculates a vibration energy vector, and a display unit that displays the calculated nodal force vector and the vibration energy vector. That. The second calculation unit adds the positive force component of the elastic force vector calculated for each element adjacent to a certain node to the component projected in the direction of the displacement vector of the node, thereby obtaining a node at the node. By calculating the elastic force vector and adding the damping force vector calculated for each element adjacent to a node to the positive component of the component projected in the direction of the velocity vector of the node, the node at the node By calculating the damping force vector and adding the positive component to the inertial force vector calculated for each element adjacent to a certain node in the direction of the acceleration vector of that node, the node at that node is added. Calculate the inertial force vector. The third calculation unit calculates an elastic energy magnitude from an inner product of the nodal elastic force vector and the velocity vector, and calculates an elastic energy vector direction from an elastic energy magnitude gradient between adjacent nodes. The elastic energy vector is calculated, the magnitude of the damping energy is calculated by the inner product of the nodal damping force vector and the velocity vector, and the vector direction of the damping energy is calculated from the gradient of the magnitude of the damping energy between adjacent nodes. Calculating the damping energy vector, calculating the magnitude of the kinetic energy from the inner product of the nodal inertia force vector and the velocity vector, and calculating the vector direction of the kinetic energy from the gradient of the elastic energy magnitude between adjacent nodes. Then, the kinetic energy vector is calculated. The display unit displays at least one of the elastic energy vector, the damping energy vector, and the kinetic energy vector.

  According to this aspect, vibration energy at each node can be derived by decomposing into respective components of elastic force, damping force, and inertial force, and each energy component can be displayed, so that the analysis accuracy can be improved.

  According to the present invention, it is possible to provide a technique for accurately analyzing vibration energy.

It is a block diagram which shows the function structure of the analyzer which concerns on embodiment. It is a figure which shows typically the calculation method of a nodal elastic force vector. It is a flowchart which shows the flow of operation | movement of an analyzer.

  Hereinafter, embodiments for carrying out the present invention (hereinafter referred to as embodiments) will be described in detail with reference to the drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and repeated descriptions are omitted as appropriate.

  FIG. 1 is a block diagram illustrating a functional configuration of an analysis apparatus 50 according to the embodiment. The analysis device 50 includes a construction unit 52, a calculation unit 54, and a display unit 56.

  Each block shown in the block diagram of the present specification can be realized in terms of hardware by an element such as a CPU of a computer or a mechanical device, and in terms of software, it can be realized by a computer program or the like. The functional block realized by those cooperation is drawn. Therefore, those skilled in the art will understand that these functional blocks can be realized in various forms by a combination of hardware and software.

  The construction unit 52 constructs a model to be calculated by the calculation unit 54 by replacing the structure to be analyzed with a finite number of small elements. Each element constituting the model is defined so that numerical analysis is possible. Specifically, for each element, a node coordinate value, an element shape, a material characteristic, and the like in the coordinate system are defined. When a two-dimensional model is targeted, a three-node element having a triangular shape or a four-node element having a quadrangular shape may be used as each element. When a three-dimensional model is targeted, a 4-node element having a tetrahedral shape, a 6-node element having a hexahedral shape, or the like may be used. The construction unit 52 can be realized, for example, by using general-purpose software based on a known technique called a preprocessor.

  The calculation unit 54 calculates values such as displacement, velocity, acceleration, elastic force, damping force, inertial force, etc., for each node of each element using the model built by the building unit 52 for each calculation step. The calculation process is repeatedly executed until the calculation end condition is satisfied. Further, the calculation unit 54 calculates the nodal force, the nodal force density, the vibration energy, and the vibration energy density at each node using the calculated values. The calculation unit 54 includes a first calculation unit 61, a second calculation unit 62, and a third calculation unit 63.

  The first calculation unit 61 attaches conditions to the model divided into a finite number of elements, and calculates the displacement, velocity, acceleration, elastic force, damping force, and inertial force at the nodes of each element from the input conditions for each calculation step. To do. The 1st calculation part 61 analyzes a model dynamically by using following formula (1) as a governing equation of each element.

  Here, {u} included in the third term on the left side represents a displacement vector at the node of each element. The first derivative with respect to time of {u} included in the second term on the left side represents the velocity vector, and the second derivative contained in the first term on the left side represents the acceleration vector. The subscript t means the time t corresponding to each calculation step. [M] in the first term on the left side is a mass matrix, [C] in the second term on the left side is a damping matrix, and [K] in the third term on the left side is a stiffness matrix. {F} on the right side is the nodal force at the node of each element. In Equation (1), the first term on the left side corresponds to an inertial force, the second term on the left side corresponds to a damping force, and the third term on the left side corresponds to an elastic force.

  The first calculation unit 61 creates a mass matrix M, a damping matrix C, and a stiffness matrix K for solving the governing equations of each element, and then creates an overall configuration matrix for representing the overall structure of the model. An unknown node displacement or the like is calculated by applying an analysis process to the equation described by the overall configuration matrix by introducing the displacement of a known node and the node force as input conditions. Thereby, the values of displacement, velocity, acceleration, elastic force, damping force, and inertial force at the nodes of each element are calculated for each calculation step. In addition, the 1st calculation part 61 is realizable by using the general purpose software based on the well-known technique called a solver, for example.

  The second calculator 62 calculates a nodal force vector at each node constituting the model using the value calculated by the first calculator 61. The nodal force (elastic force, damping force, inertial force) calculated by the first calculation unit 61 is a calculation result calculated for each element. Therefore, the second calculation unit 62 calculates the nodal force vector at the node by adding the nodal force values obtained for each of the plurality of elements adjacent to the specific node. In this specification, “node force vector” means “node elastic force vector”, “node damping force vector”, “node inertia force vector” representing the elastic force, damping force, and inertial force at each node constituting the model. Are sometimes used as generic terms.

  FIG. 2 is a diagram schematically illustrating a method of calculating the nodal elastic force vector E. FIG. 2 shows a first element 11, a second element 12, a third element 13, and a fourth element 14, which are four-node elements having a quadrangular shape, as elements constituting the model. Also, nine nodes from the first node 21 to the ninth node 29 are shown as nodes in each element. In this embodiment, an example in which a four-node element is used is shown, but those skilled in the art can also apply to models having elements having other shapes or elements of different types (dimensions). It will be obvious to you.

  This figure shows a method of calculating the nodal elastic force vector E at the fifth nodal point 25 shared by the four elements from the first element 11 to the fourth element 14. The elastic forces E1 to E4 shown in this drawing are the elastic forces at the fifth node 25 for each of the first element 11 to the fourth element 14, and for example, the first elastic force E1 is the first force of the first element 11. This is the elastic force at the 5 node 25. The nodal elastic force vector E was projected by projecting the first elastic force E1, the second elastic force E2, the third elastic force E3, and the fourth elastic force E4 in the direction of the displacement vector u at the fifth node 25. It is calculated by adding only positive components in the direction of the displacement vector u. Therefore, the nodal elastic force vector E is expressed by the following equation (2).

Here, the vector Ei represents the elastic force at the node for each of a plurality of elements i adjacent to the node for which the node elastic force vector E is obtained, and the variable n represents the number of elements adjacent to the node. Represent. In the example shown in FIG. 2, the vector Ei is the first elastic force E1, the second elastic force E2, the third elastic force E3, and the fourth elastic force E4, and the variable n is adjacent to the fifth node 25. The number of elements is 4. In the example shown in FIG. 2, among the elastic forces E1 to E4, the first elastic force E1, the second elastic force E2, and the fourth elastic force E4 have a positive inner product with the displacement vector u, while the third elastic force E3 has a negative inner product with the displacement vector u. Therefore, the second calculation unit 62
Only the first elastic force E1, the second elastic force E2, and the fourth elastic force E4 that have a positive inner product with the displacement vector u are added, and the third elastic force E3 is not added. Thus, the 2nd calculation part 62 calculates the nodal elastic force vector in each nodal point.

  The second calculator 62 calculates the nodal damping force vector and the nodal inertia force vector at each node by the same method. At this time, the nodal damping force vector is calculated by projection onto a velocity vector, and the nodal inertia force vector is calculated by projection onto an acceleration vector. The nodal damping force vector is calculated by projecting each damping force calculated for each element adjacent to a certain node in the direction of the velocity vector and adding only the positive components in the direction of the projected velocity vector. . In addition, the node inertia force vector is calculated by projecting each inertia force calculated for each element adjacent to a certain node in the direction of the acceleration vector, and adding only the positive components in the direction of the projected acceleration vector. Is done.

  The second calculator 62 may calculate a nodal force density vector in addition to the nodal force vector. The nodal force density vector is a nodal force vector per unit volume, and can be obtained by dividing the nodal force vector by the volume of each element. That is, the second calculator 62 may calculate a nodal elastic force density vector, nodal damping force density vector, and nodal inertia force density vector from the nodal elastic force vector, nodal damping force vector, and nodal inertia force vector.

  The 3rd calculation part 63 calculates the magnitude | size of the vibration energy in each node using the obtained nodal force vector and velocity vector. The magnitude of vibration energy can be obtained by calculating the inner product of the nodal force vector and the velocity vector. At this time, the third calculator 63 calculates the magnitude of vibration energy based on the respective contributions of elastic force, damping force, and inertial force. The third calculator 63 calculates the magnitude of the elastic energy from the inner product of the nodal elastic force vector and the velocity vector, calculates the magnitude of the damping energy from the inner product of the nodal damping force vector and the velocity vector, The magnitude of kinetic energy is calculated from the inner product of velocity vectors.

  The third calculator 63 calculates the vector direction of the vibration energy from the gradient of the magnitude of vibration energy between adjacent nodes, and calculates the vibration energy vector from the magnitude and vector direction of the vibration energy. At this time, the 3rd calculation part 63 calculates the vector direction of vibration energy about each of an elastic force, a damping force, and an inertial force, and calculates the vibration energy vector about each. Thereby, the 3rd calculation part 63 calculates an elastic force energy vector, a damping force energy vector, and a kinetic energy vector.

  The third calculator 63 may calculate vibration energy density in addition to calculation of vibration energy. The vibration energy density can be obtained by calculating the inner product of the nodal force density vector and the velocity vector. That is, the third calculation unit 63 may calculate the elastic energy density, the damping energy density, and the kinetic energy density from the nodal elastic force density vector, the nodal damping force density vector, and the nodal inertia force density vector. Further, the vibration energy density vector may be calculated by calculating the vector direction of the vibration energy density from the gradient of the vibration energy density between adjacent nodes.

  The display unit 56 visualizes and displays the values of the nodal force vector and the vibration energy vector calculated by the calculation unit 54 on the constructed model. For example, the display unit 56 arranges arrows indicating the directions of the nodal force vector and the vibration energy vector corresponding to the nodal points constituting the model, and displays the arrow according to the magnitude of the nodal force vector and the vibration energy vector. The calculation result is visualized and displayed by changing the color and size.

  The display unit 56 may display values based on respective contributions of elastic force, damping force, and inertial force among the nodal force vector and the vibration energy vector. For example, when only the value based on the contribution of the elastic force is displayed, the display unit 56 displays only the nodal elastic force vector and the elastic energy vector on the model. The display unit 56 may display a nodal force density vector or a vibration energy density vector instead of or in addition to the nodal force vector or the vibration energy vector.

  Note that the analysis device 50 may include an output unit that outputs the calculation result instead of or in addition to the display unit 56. The output unit may output the calculated value of the nodal force vector or elastic energy vector as a numerical value to the outside of the analyzing device 50, or may analyze image data or the like in which the nodal force vector or elastic energy vector is visualized. You may output to the outside.

The operation of the analysis device 50 configured as above will be described.
FIG. 3 is a flowchart showing a flow of operation of the analysis apparatus. First, a model to be analyzed is constructed (S10), and displacement, velocity, acceleration, and nodal force (elastic force, damping force, inertial force) are calculated for each element constituting the model (S12). Next, using the value calculated for each element, a nodal force vector (nodal elastic force vector, nodal damping force vector, nodal inertia force vector) is calculated for each node (S14). A vibration energy vector (elastic energy vector, damping energy vector, kinetic energy vector) is calculated for each node from the obtained nodal force vector and velocity vector (S16). Further, a nodal force density vector is calculated by dividing the nodal force vector by the unit volume (S18), and a vibration energy density vector is calculated from the nodal force density vector and the velocity vector (S20). The obtained nodal force vector, vibration energy vector, etc. are visualized and displayed (S22).

  According to the present embodiment, since the nodal force and vibration energy obtained as an analysis result can be visualized separately for each component of elastic force, damping force, and inertial force, the accuracy of vibration analysis can be improved. In general, the vibration countermeasures for each component of elastic force, damping force, and inertial force can be different, so obtaining analysis results for each component is very useful in considering structural design changes, etc. is there.

  In addition, according to the present embodiment, the force and energy at each element are not calculated, but the force and energy at each node are calculated, so the node is also applied to a model configured by combining different types of elements. Force and vibration energy can be visualized. For this reason, even when multiple types of elements are mixed in order to model a complex structure, the load flow and vibration energy flow from the load input point to the response point throughout the structure It can be visualized. As a result, the accuracy of vibration analysis can be improved, and useful information can be provided for studying design changes and the like of structures.

  In the above, this invention was demonstrated based on embodiment. It will be understood by those skilled in the art that the present invention is not limited to the above-described embodiment, and various design changes are possible, various modifications are possible, and such modifications are within the scope of the present invention. By the way.

  50 analysis device, 54 calculation unit, 56 display unit, 61 first calculation unit, 62 second calculation unit, 63 third calculation unit, E nodal elastic force.

Claims (1)

Conditions are applied to a model divided into a finite number of elements with a node as a boundary, and the displacement vector, velocity vector, acceleration vector, elastic force vector, damping force vector, and inertial force are calculated for each element. A first calculation unit for calculating a vector;
A second calculation unit for calculating a nodal force vector at the node from values calculated for a plurality of elements adjacent to the nodal point;
A vibration energy vector is calculated by calculating a vibration energy magnitude from an inner product of the nodal force vector and the velocity vector, and calculating a vibration energy vector direction from a gradient of the vibration energy magnitude between adjacent nodes. 3 calculation units,
A display unit for displaying the calculated nodal force vector and the vibration energy vector;
With
The second calculator is
Calculate the nodal elastic force vector at the nodal point by adding only the positive component of the elastic force vector calculated for each element adjacent to the nodal point and the component projected in the direction of the displacement vector of the nodal point,
By adding only the positive component of the component projected in the direction of the velocity vector of the node to the damping force vector calculated for each element adjacent to the node, the node damping force vector at the node is calculated,
The inertial force vector calculated for each element adjacent to a certain node is added to only the positive component of the component projected in the direction of the acceleration vector of the relevant node, thereby calculating the nodal inertial force vector at the relevant node,
The third calculator is
The elastic energy vector is calculated by calculating the elastic energy magnitude from the inner product of the nodal elastic force vector and the velocity vector, and calculating the elastic energy vector direction from the gradient of the elastic energy magnitude between adjacent nodes. ,
The magnitude of damping energy is calculated from the inner product of the nodal damping force vector and the velocity vector, and the damping energy vector is calculated by calculating the vector direction of the damping energy from the gradient of the magnitude of the damping energy between adjacent nodes. ,
Calculate the kinetic energy from the inner product of the node inertia force vector and the velocity vector, calculate the kinetic energy vector direction from the gradient of elastic energy between adjacent nodes, and calculate the kinetic energy vector. ,
The analysis device, wherein the display unit displays at least one of the elastic energy vector, the damping energy vector, and the kinetic energy vector.

Images