基于固定界面模态综合法的刚柔耦合理论手册(UM)

Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 1 11.  Simulation of dynamics of flexible bodies using UM FEM .......................................... 2  11.1.  Basic ideas and methods........................................................................................................... 2  11.1.1.  Introduction ......................................................................................................................... 2  11.1.2.  Kinematics........................................................................................................................... 2  11.1.3.  Calculation of stress and strain............................................................................................ 4  11.2.  Installation, preparing data, workflow................................................................................... 6  11.2.1.  Creating a finite element model in ANSYS and data exchange.......................................... 6  11.2.1.1.  Preparing data in the ANSYS environment .................................................................... 6  11.2.1.2.  Creating stress and strain sensors.................................................................................... 9  11.2.1.3.  ANSYS-UM data exchange ......................................................................................... 11  11.2.2.  Creating of finite element model in MSC.NASTRAN and data exchange....................... 15  11.2.2.1.  General information ...................................................................................................... 15  11.2.2.2.  Software modules and workflow................................................................................... 15  11.2.2.3.  Preparing of data in MSC.PATRAN/NASTRAN environment.................................... 17  11.2.2.4.  MSC.NSATRAN-UM data exchange. .......................................................................... 24  11.2.3.  Особенности подготовки данных в программе МКЭ ..................错误！未定义签。  11.2.3.1.  Выбор интерфейсных узлов .......................................................错误！未定义书签。  11.2.3.2.  Контроль нормалей к поверхностям оболочек и пластин .......错误！未定义书签。  11.3.  Wizard of flexible subsystems ............................................................................................... 26  11.3.1.  Animation window............................................................................................................ 27  11.3.2.  Control form...................................................................................................................... 27  11.3.2.1.  General tab .................................................................................................................... 28  11.3.2.2.  Solution tab.................................................................................................................... 30  11.3.2.3.  Image tab ....................................................................................................................... 33  11.3.2.4.  Position tab .................................................................................................................... 34  11.4.  Adding the flexible subsystem into a hybrid model............................................................. 35  11.4.1.  Adding the flexible subsystem .......................................................................................... 35  11.4.2.  Flexible subsystem inspector............................................................................................. 36  11.4.2.1.  General tab .................................................................................................................... 36  11.4.2.2.  Position tab .................................................................................................................... 36  11.4.2.3.  Solution tab.................................................................................................................... 37  11.4.3.  Features of adding joints and forces.................................................................................. 38  11.5.  Analysis of dynamics of flexible subsystem in model .......................................................... 39  11.5.1.  Object simulation inspector............................................................................................... 39  11.5.1.1.  Simulation tab................................................................................................................ 39  11.5.1.2.  The Image tab................................................................................................................ 41  11.5.2.  Variables............................................................................................................................ 42  11.5.2.1.  Coordinates.................................................................................................................... 42  11.5.2.2.  Linear variables ............................................................................................................. 42  Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 2 11. Simulation of dynamics of flexible bodies using UM FEM 11.1. Basic ideas and methods 11.1.1. Introduction UM FEM module is a set of software tools that are built-in UM Input and UM Simulation programs. The module gives a user a possibility to introduce flexible bodies under large displacements into a model of mechanical system. Flexible displacements are supposed to be small in the body-fixed frame of reference and could be described in terms of linear finite-element analysis (FEA). Introducing flexible bodies into a model of mechanical system is used for creating the more detailed models and obtaining more accurate results of simulation. In some cases modeling the system with the help of rigid bodies only is too rough approximation of a real system. Then some bodies of the model should be considered as flexible, for example, car body and chassis of transport machines. Using flexible bodies to obtain more accurate solution (coordinates, accelerations) and widen its spectrum that might be important in some cases, for example, for analysis of vibrations and durability of machines. UM FEM needs that UM Subsystems module is also being installed on your computer. As well as it is necessary that a FEA preprocessor and solver are available on your computer. The present UM FEM version supports import from following FEA software: • ANSYS software version 5.5 and later; • MSC.NASTRAN 2005 and MSC.NASTRAN 2007. It supposes that you have at least basic skills in using ANSYS software and have an idea of modal approach. In this section some basic information concerning methods of simulation of flexible bodies in UM FEM is presented. Mathematical model of a flexible body is based on using the following methods: • subsystem technique, • floating frame of reference method, • finite-element method, • Craig-Bampton method. Every flexible body is considered as a separate subsystem that is why assembly of composite1 model is similar to assembly of multibody model. Before assembly the preliminarily step of preparing the necessary data of FE-model of flexible bodies should take place. Flexible bodies/subsystems can interact with any other rigid or flexible bodies with the help of joints and force elements. 11.1.2. Kinematics Kinematics of flexible bodies is described with the help of so called floating frame of reference CS1. Kinematical formulas are noted in this floating frame of reference. Position of certain point K of the flexible body in the global CS0 is defined as follows (Fig. 11.1): )( 1101 0 01 0 kkk dρArr ++= , (11.1) where r01 is radius vector of the origin of CS1 in CS0, A01 is transformation matrix, ρk is radius vector of point K of undistorted flexible body in CS1, vector dk presents elastic displacements of the point, superscript denotes the coordinate system in which vectors are given. Elastic properties of the flexible bodies relatively to the CS1 are described with the help of finite- element method. The present UM FEM version supports import of data about flexible bodies from ANSYS software version 5.5 and later and MSC.NASTRAN 2005. 1 Composite or hybrid model includes both rigid and flexible bodies Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 3 z1 y1 z0 1 r01 rk ρk dkuk K’ K x0 x1 0 y0 Figure 11.1. Floating frame of reference Small elastic displacements are presented as a sum H of possible modes/shapes of flexible body: Hwhx ==∑ = H j jj w 1 , (11.2) where x is nodal degrees of freedom of the flexible body, is the possible mode, wj is the modal coordinate that describes flexible displacements correspond to mode j. The matrix H is called modal matrix. jh According to the Craig-Bampton method the modal matrix is formed as a combination of eigenmodes and static modes. The method consists of four steps. 1) Choice of interface (boundary) nodes of a finite-element scheme. 2) Successive calculation of static modes. Static modes are static shapes obtained by given each boundary d.o.f. a unit displacement while holding all other boundary d.o.f. fixed. 3) Calculation of eigenmodes while holding all interface nodes fixed; 4) Calculation of the mass matrix and the stiffness matrix, orthonormalization of the eigenmodes and static modes. The short description of the each step is given below. Choice of interface nodes. Flexible body/subsystem interacts with other bodies of the model via joints and force elements. It is recommended that every attachment point should be situated in the node of finite-element mesh. Very these nodes, where joints and force elements are attached to, should be chosen as interface nodes. Such an approach helps to create joint constrains correctly and quite accurate describe flexible displacements that determine force in force element. It is necessary to choose interface nodes so as during calculation of each static mode the immobility of the subsystem was guaranteed. Calculation of static modes. The number of static modes is equal to number of d.o.f. in interface nodes. During this procedure interface nodes are held fixed and static modes are obtained by given each interface d.o.f. a unit displacement/rotation. Calculation of eigenmodes. Eigenmodes of flexible body are obtained from the solving the generalized eigenproblem: 0)( =− yMС λ , (11.3) where С is the stiffness matrix, M is the mass matrix, λ is the eigenvalue, y is the eigenmode. If these matrices are of a full rank the equation (11.3) has N solutions, where N is the number of rows that correspond to nodal d.o.f. The mass matrix of the flexible subsystem may be formed based on shape functions of finite elements or may have a diagonal form as a result of using lumped model. A user determines number and shapes of used eigenmodes. As a rule a set of eigenmodes includes lower eigenmodes. Calculation of generalized matrices, orthonormalization of modes. Generalized mass and stiffness matrices are calculated using the modal matrix H: Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 4 MHHM T= , CHHC T= where M is the generalized mass matrix, C is the generalized stiffness matrix. The final step of the preparing set of modes is the orthonormalization of columns of the modal matrix based on eigenvalue problem solution with generalized mass and stiffness matrix: 0)( =− yMC λ (11.4) Transformed set of modes is formed based on the equation: YHH = (11.5) Diagonal form of transformed generalized matrices leads to minimal CPU efforts during the integration of equations of motion. It is the basic advantage of such an approach. Another aim of such transformations is exclusion modes that correspond to movement of the flexible subsystem as a rigid body. It is necessary since movement the flexible subsystem as rigid one is defined by floating frame of reference CS1. Zero eigenvalues correspond to rigid body modes of flexible subsystem (11.4). 11.1.3. Calculation of stress and strain Let’s consider the discrete expressions of elasticity theory used in the finite elements method: e i e i e i e i uxBε )(= , e i e i e i e i e i e i uBDεDσ == , (11.6) where , , is matrix-columns of nodal degrees of freedom of strains and stresses of i-th finite element, is matrix expressing strain field of the finite element with the nodal displacement, is elasticity matrix of the finite element which is generated according to Hooke's law, is matrix-column of coordinates of finite elements nodes. Sizes of the matrices depend on finite element type. e iu e iε e iB e iσ e iD e ix If nodal displacements are represented as the sum (11.2), strains and stresses of a finite element can be represented by following expressions: wHhhxBwHxBε εε ei H j j e ji H j j e ji e i e i e i e i e i e i ww ∑∑ == ==== 11 )()( , wHhhxBDwHxBD σσσ ei H j j e ji H j j e ji e i e i e i e i e i e i e i e i ww ∑∑ == ==== 11 )()( , (11.7) where is the part of j-th mode which corresponds to nodal degrees of freedom of i-th finite element. Matrices-columns and represent stresses and strains from nodal displacements of the finite element which are correspond to the mode when value of the modal coordinate wj=1. These matrices- columns are called element solutions. e jih εe jih σe jih e jih So far as are constant matrix, they are not used for simulation after calculation of and . Therefore, stresses and/or strains can be calculated during integration of equations of motion of flexible body if stresses and/or strains modal matrices are calculated correspond to the expressions (11.7). )(, ei e i e i xBD εe jih σe jih Matrices-columns and corresponded to the mode of a flexible body are calculated by FEA software. Before using in UM software, they are transformed similarly to the matrices-columns based on the expressions (11.4, 11.5). εe jih σe jih jh jh Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 5 j k im l Figure.11.2. To example of calculation of nodal stresses Nodal stresses or strains are calculated by FEA programs based on values which are calculated for elements including the concerned node. The simple averaging of values is often used. For example, if the node with index i is belonged to the four finite elements with the indices j,k,l,m (Fig.11.2), then nodal stress are calculated as i Mb e bi e mi e li e ki e ji n i N i ∑ ∈=+++= σ σσσσσ 4/)( , where is nodal stress, is the stress components in the node i of the finite element with the index j, Mi is the set of indices of the finite elements including the node i, Ni is count of finite elements including the node i. n iσ ejiσ UM 5.0 imports solutions for elements. The nodal solutions are calculated as average values in the elements containing the node. Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 6 11.2. Installation, preparing data, workflow UM FEM installation package includes the following items: • software for data import from ANSYS: o macro file um.mac for ANSYS, which is written in APDL (ANSYS Parametric Design Language); o stand alone program for data transformation ansys_um.exe; • software for data import from MSC.NASTRAN: o file umfum.alt with procedures which are written in DMAP language (Direct Matrix Abstraction Program); o stand alone program for data transformation nastran_um.exe; • wizard of flexible subsystems built in uminput.exe program; • software procedures for handling and simulation of dynamics of flexible bodies that are built in uminput.exe and umsimul.exe. Simulation of dynamics of flexible bodies supposes the following steps to be done. 1) Creating the FEA model of the flexible body to analyze in the external FEA software. 2) Choosing the interface nodes, calculation of the eigenmodes and static modes according to Craig-Bampton method. 3) Exporting data from external FEA software and its transformation to UM format. 4) Including the flexible subsystem into hybrid model with the help of UM Input program. 5) Simulation of dynamics of the hybrid model with the help of UM Simulation program. Every step is considered in the next items. Data preparing in ANSYS is described in 11.2.1 item, 11.3.1 is devoted to work in MSC.NASTRAN. 11.2.1. Creating a finite element model in ANSYS and data exchange 11.2.1.1. Preparing data in the ANSYS environment The whole workflow of the preparing input data for models that include flexible bodies is shown in Fig. 11.3. Let us consider basic steps of this procedure. The first step is executed under ANSYS environment. According to instructions to ANSYS software the work directory and JobName are chosen. JobName is a name of all the files for certain FEA model. After creating the FEA model and choosing interface nodes the macros um.mac is executed. This macros has commands for calculation of eigenmodes and static modes, as well as calculation and exporting mass and stiffness matrices. As a result of um.mac execution several files are created: standard ANSYS result file JobName.rst, JobName.full that contains matrices of a flexible body corresponded to fixed interface nodes, JobName.free that contains matrices of a free body, and JobName.mlmp with a diagonal mass matrix of a free body. In dependence of arguments of the um.mac the JobName.mlmp file may not be created. For example, if Beam is the task name then files Beam.rst, Beam.full and Beam.free will be created in the working directory after calculations. Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 7 ANSYS • Creating a FEA model of a flexible body • Choosing interface nodes • Running um.mac macros under ANSYS environment JobName.rst JobName.full JobName.free JobName.mlmp UM.MAC macros • Calculating eigenmodes and static modes • Calculating mass matrix of a free body ANSYS_UM.EXE • Conver ting file formats • Calculating generalized mass and stiffness matrix • Orthonormalization of the modes; excluding rigid body modes Wizard of flexible subsystems (UMINPUT.EXE) • Visual control of modes and other results • Excluding shapes from the final set if necessary • Orthonormalization of modes; excluding rigid body modes UMINPUT.EXE • Loading input data, description of a hybrid model • Generation of equations of motion • Compilation of equation of motion UMSIMUL.EXE • Simulation of dynamics and linear analysis input.fum input.fss input.dat UMTask.dll input.fss Figure 11.3. Data preparing workflow Universal Mechanism 5.0 Part 11. UM FEM module: flexible bodies 8 After installation the um.mac file is situated in the {um_root}\bin directory. Copy the um.mac file to the directory that is selected as a default directory for the macro files in ANSYS. It is usually .\docu directory from the ANSYS root directory. Otherwise you should indicate the path to the um.mac file using PSEARCH command: /PSEARCH, path_to_um.mac. The second step of the data preparing is fulfilled in the ansys_um.exe program, w