07產(chǎn)品用戶手冊英文手冊6loadconstraint

1、New eXperience of GeoTechnical analysis SystemChapter 6 Load ConstraintTABLE OF CONTENTSSection 1.LoadSection 2.Boundary and Constraint ConditionsSection 3.Pore Pressure / Initial ConditionANALYSIS REFERENCEChapter 6. Load/ConstraintLoadThe usable structural loads in GTS NX can be largely classified

2、 into force, gravity, displacement and thermal expansion due to temperature, as shown in table 6.1.1TypesNodal force/moment Surface/edge pressure load Surface/edge water pressure load Beam loadGravity Specifieddisplacement/velocity/acceleration Temperature loadTemperature gradient Prestress andiniti

3、al equilibrium forceApplicable range node1D element, 2D element, 3D element 2D element, 3D elementBeam elementAll elements with mass nodenode, 1D element, 2D element, 3D element Beam element, shell elementtruss element, beam element, plane stress element, plane strain element, axisymmetric solid ele

4、ment, solid element Nodal force Nodal forces are the most basic loads and have 3 force component inputs and 3 moment component inputs for each node. The direction can be defined about an arbitrary coordinate system. Pressure load The pressure load is input as a distributed force form for an element

5、face or edge. The surface pressure load is applicable for 2D or 3D elements and the edge pressure load is applicable for 1D or 2D elements. The input direction can be specified as an arbitrary coordinate axis direction, arbitrary vector direction or normal direction. Figure 6.1.1 displays the pressu

6、re load acting on various elements.Section 1. Load | 2391.1Structural LoadTable 6.1.1 Usable loads in GTS NXSection 1Chapter 6. Load/ConstraintANALYSIS REFERENCEpressure on edgepressure on surface Water pressure loadGTS NX can consider water pressure that occurs from the defined water level of a m.

7、Waterpressure is added as an edge pressure load for 2D problems and as a surface pressure load for 3D problems.The pressure size needed for calculating the water pressure is determined as follows: Same size as the pore pressure defined on the target edge/surface Hydrostatic pressure due to user inpu

8、t water level position, z phreatic :-z for gravitational direction p = r gf( z phreatic - z )GTS NX supports the automatic water pressure method, which applies an automatic water pressure toalledges/surfaces. In this case, only the parts below the water level receive a pressure loadautomatically. On

9、 the other hand, to respond to the ming needs for general water pressureconditions, the manual setting of water pressure for necessary edges/surfaces is also provided.Phreatic line Self weight due to gravityThe gravity is used to m elements with mass.the self weight or inertial force of a structure

10、and can be applied to all240 | Section 1. LoadFigure 6.1.2 Water pressure generated by to water levelFigure 6.1.1 Pressure load acting on various elementsANALYSIS REFERENCEChapter 6. Load/ConstraintGravity is applied to all activated elements. It is also automatically applied to elements added in th

11、e construction stage. Likewise, it is automatically removed when the element becomes inactive.Analysis considering pore pressu external force.as the self-weight due to degree of saturation as an additional Specified displacement/velocity/acceleration Specified displacement is assigned to the displac

12、ement of particular nodes and is used when the nodal position after deformation is known. Specified displacements generate structural deformation and are classified as loads, but they have similar characteristics as boundary conditions such as the generation of confining force.Setting the total DOF

13、of the target problem as u , it can be divided into DOF with/without assignedAspecified displacement as follows:ìu ü(6.1.1)u =Fíu ýAî S þ: DOF without assigned specified displacement: DOF with assigned specified displacementu FuSThe stiffness matrix can also be classifi

14、ed and expressed using the same principle:= éKFFFSFK ù ìu üìf ü= f=FK uú íuAýíf ýAA A êKKë SFSS ûî S þî S þ(6.1.2)uS in the equation above is a determined value and thus the 2nd row of the stiffness matrix does

15、 nothave meaning. Using u to rearrange the 1st row, the load due to specified displacement can beScalculated as follows:K FF u F = f F - K FS u S(6.1.3)Specified velocity and acceleration loads can be assigned in dynamic analysis. Specified velocity and acceleration conditions are coupled with time

16、integration and can be converted to the specified displacement condition. The converted condition is applied to the matrix operation as explained above.Section 1. Load | 241Chapter 6. Load/ConstraintANALYSIS REFERENCE Temperature load Temperature load can be expressed as the difference DT between th

17、e initial temperature and final temperature, and the strain = (Tm )DT is generated by the coefficient of thermal expansion (Tm )determined by the material temperature Tm . Hence the initial and final temperature of each structureneeds to be defined. The method of defining the temperature is listed i

18、n table 6.1.2.TypesApplicable rangetruss, embedded truss, beam, geogrid, plane stress, plane strain, shell, solidElement temperature Temperature gradient Temperature gradient load can only be applied to beam elements and shell elements, which can consider bending stiffness. For beam elements, the te

19、mperature difference and distance of the outermost portion is input with reference to the y axis and z axis of the element coordinate system. For shell elements, the temperature difference between the top and bottom faces and the plate thickness is input to consider the temperature gradient load. Pr

20、estress and initial equilibrium force GTS NX uses the prestress function to apply the resultant force or stress as an initial condition, depending on the element type. If the inital stress is given as such, an internal force corresponding to the initial stress is generated. If the final external str

21、ess is not in equilibrium with the initial internal force, changes in strain and stress occur according to that difference.The initial equilibrium force is a function that generates the internal force, corresponding to the initial stress applied by prestress, as an external force. The initial equili

22、brium force for the element e , with the reflected initial stress from prestress, is expressed as follows:òf e= B dWText,eq0(6.1.4)WeIf additional external forces do not exist, the initial equilibrium force and initial stress form equilibrium and so, the initial state is maintained. Also, GTS N

23、X can assume the initial stress applied on an element to be the stress generated by gravity. When this assumption is applied, the load distribution factor considering self weight is applied when the element is removed from the construction stage.242 | Section 1. LoadNodal temperaturenodeTable 6.1.2

24、Temperature types that can be defined on structuresANALYSIS REFERENCEChapter 6. Load/ConstraintPretension can be used for 1D elements to maintain the given axial direction resultant force. The axial resultant force of the element in the load applied step and the corresponding element internal force

25、does not change. Static load Static loads in GTS NX are used for linear/nonlinear static analysis and consolidation analysis, and are composed of combinations of the load types introduced above. The load is applied differently for linear static analysis and nonlinear analysis. Linear static analysis

26、Linear static analysis is performed in one stage for the total load and so, the total static load is applied. Nonlinear static analysis/construction stage analysisThe load is applied proportional to a load scale 0 £ lI £ 1 defined by each construction stage or as aunit of singular analysis

27、. The total load vector in nonlinear analysis is defined in the following form.I int ,0I å extf (l ) = (1- l ) f+ lfjext I(6.1.5)jHere, f represents the external force vector due to the j th load, and fjis the internal forceextint ,0corresponding to the initial state of nonlinear analysis or ea

28、ch stage of construction stage analysis,which can be calculated as the sum of initial internal forces for each element ( f ):eintint ,0 å int 0 0f=f ( ,u , Le)(6.1.6)eWhen the load scale is l0 = 0 , the total external forces and initial internal forces are in an equilibrium state and when the l

29、oad scale is lI = 1 for the final state of the stage, the total external force is the total sum of the given load combinations. Particularly, the continuity of the external force isguaranteed when an element is added or removed from the construction stage and so, this canprevent deterioration of con

30、vergence due to discontinuous load properties in nonlinear analysis.The load scale corresponding to the I th load increment, lI can be set to have an even interval or anarbitrary value between '0' and'1'.Section 1. Load | 2431.2Static/Dynamic Load DefinitionChapter 6. Load/Constraint

31、ANALYSIS REFERENCE Dynamic load Dynamic loads are used to apply various changing load conditions for linear/nonlinear time history analysis. The total load vector in time history analysis is defined as the following function of time, t .å=T (t) fjf (t) extjext(6.1.7)jHere, Tj (t) is the j th lo

32、ad scale and it is generally defined as a tabular data form for time, or byinputting coefficients for a particular function (equation 6.1.8):Tj (t) = ( A + C t)esin(2p f t + P)- Dt (6.1.8)244 | Section 1. LoadANALYSIS REFERENCEChapter 6. Load/ConstraintStatic loads are used for construction stage st

33、ress analysis, and the body force due to self weight is automatically reflected in the total external force for the addition and removal of elements in each stage. Load distribution factor When partial elements are removed in a construction stage due to excavation, GTS NX supports construction stage

34、 analysis that uses the load distribution factor (LDF) such that the effects of element removal are reflected gradually for multiple construction stages.The internal forces and body forces from the removed elements in a construction stage can beremoved gradually in later stages and the load distribu

35、tion factor scontrols the size of the forceLDFthe removed element once shared. Ultimately when sis '0', the effects of the removed elementLDFcompletely disappear (figure 6.1.3). The LDF of each stage is defined by the user:gDEL : Residual force contributionfrom deleted elementsi,LDF : Load d

36、istribution factorElement RemovalgDELfLDF = si LDF gDEL(0 < si LDF < 1)fLDF = 0(si LDF = 1)Stage (i+1)Stage (i)Stage (i-1)The loads which were shared by the removed element be expressed as follows:as external forces in later stages, and canfLDF = sLDF gDELNDg= åB dW - WòWTeDELG(6.1.9

37、)eef L DF: Load distribution external force vectorg D EL: Load sharing vector for the unbalanced force due to the removed element: Body force due to element self-weightW eGSection 1. Load | 245Figure 6.1.3 Construction stage load from load distribution factor (LDF)1.3Construction Stage Analysis Load

38、Chapter 6. Load/ConstraintANALYSIS REFERENCEThe nonlinearity of the system often results from material nonlinearity or geometric nonlinearity. In addition, there are cases where nonlinear analysis is needed for systems with load nonlinearity. For example, when the load direction changes with the str

39、uctural displacement or when the load size is dependent on the structural behavior. GTS NXL can reflect the effects of follower loads, where theload direction changes with the structural displacement when perfor analysis.geometric nonlinear Follower force When the nodal force direction is determined

40、 by the relative position of two different points, its size and direction are as follows:= F (xkb - xjb )(6.1.10)f = Fnbbx - xkjj, k : Nodes that determine the load direction: Load component ( x , y , z )bDifferentiating fb for x ja is as follows: ¶fbæ)(xkb - xjb ) dö÷= F ça

41、b x j(6.1.11)-÷¶xjaøUsing the same process, the derivativeof x cankabecalculated and as a result, an asymmetricstiffness matrix is composed. This stiffness due to the nonlinearity of load is called the load stiffness, and it is generally a matrix with a strong asymmetry.The direction

42、of the pressure acting normal to a particular face of the structure changes as the direction of that face changes. Figure 6.1.4 displays the large deformation effects when the forces acting on a structure face are normal or in a specified direction.Normal pressurePressure in specified direction246 |

43、 Section 1. LoadFigure 6.1.4 Directional change of pressure load due to large deformation1.4Nonlinearity of LoadsANALYSIS REFERENCEChapter 6. Load/ConstraintThe load stiffness calculation process1 for pressure acting normal to the element face is as follows. The nodal force of the I th node is integ

44、rated and calculated using the pressure p(x ,h ) = p J N J (x ,h ) as follows:f I = òò p(x ,h) ¶x ´ ¶x N I (x ,h)dx dh(6.1.12)¶x ¶hThe geometric stiffness KIJ can be calculated by differentiating the equation above at a nodal position:¶f Ié ¶f I¶

45、;f I¶f I ù(6.1.13)K = ¶xJ =IJú¶xJ3 ûEach column composing the stiffness can be found from the derivative of x in equation (6.1.12), which changes with the displacement:éæê+ ¶x ´ æ ¶ ¶x öù¶f I(6.1.14)x h´ç&

46、#250; N d dI÷x ¶hJøúûèjApart from this, beam element load, gravity, rotational inertial force etc. have follower force effects, and the changing effects according to the displacement for each load can be selected for consideration. Table 6.1.3 displays the load types th

47、at can consider the follower force effects:TypeApplicable range/methodWhen load acts normal to an element face / Use load stiffness(Water)pressure loadUse load stiffnessGravity1 Hibbit, H D , “Some follower forces and load stiffness”, International Journal for Numerical Methods in Engineering, Vol 4

48、, 1979Section 1. Load | 247Beam loadWhen defined with reference to ECS / Use load stiffnessNodal forceWhen direction is defined by two nodes / Use load stiffnessTable 6.1.3 Loads that can consider the follower forceChapter 6. Load/ConstraintANALYSIS REFERENCEBoundary and Constraint ConditionsConstra

49、int conditions can be largely divided into single-point constraints and multi-point constraints. Single-point constraints represent constraint conditions that are applied to a single node, and multi- point constraints represent a constraint that is applied between multiple DOFs to form a particular

50、relationship.Single node constraints selectively fix the DOF components of individual target nodes, resulting in the removal of that DOF. Single node constraints are generally applied where actual displacement does not occur or is used to set the symmetry condition.Apart from this, single node const

51、raints can also be used to remove DOFs that should not be reflected in the analysis. This method is the same as removing the singularity of the stiffness matrix, and setting the direction for constraint condition application appropriately is important. For example in the figure below, the node where

52、 the two truss elements meet only has an axial DOF and thus DOFs in the other directions should not be reflected in the analysis. These DOFs need to be appropriately constrained and the singularity needs to be removed from the stiffness matrix, but an appropriate constraint direction cannot be speci

53、fied when the coordinate axis is defined in the x-y coordinate system, as shown in the figure. Hence, a new nodal displacement coordinate system needs to be defined, including the element axial direction and the vector n normal to it, and the n direction needs to be constrained to achieve an appropr

54、iate constraint condition required for analysis.ynTruss 2xTruss 1248 |Section 2. Boundary and Constraint ConditionsFigure 6.2.1 Example of nodal displacement coordinate system use2.1Single Node ConstraintSection 2ANALYSIS REFERENCEChapter 6. Load/ConstraintMultiple node constraints use the linear re

55、lationship between multiple nodal DOFs to apply theconstraint condition, and teral linear relationship form is as follows:(6.2.1)Rju j = 0: Linear relationship coefficient: DOF related to constraint conditionRjujWhen there are multiple node constraints, it can be expressed in the following matrix fo

56、rm:(6.2.2)R M u M = 0To apply the multiple node constraint to simultaneous equations, uis classified into theMindependent and dependent DOFs, and the dependent DOFs are eliminated from the simultaneous equation. First, the DOFs that are involved in the multiple node constraint are classified into th

57、eindependent DOF u and dependent DOF u .IDìu ü= R(6.2.3)u =, RIí ýRMMIDîuD þUsing the equation above, equation (6.2.2) can be expressed as follows:(6.2.4)R I u I + R D u D = 0If the R inverse matrix exists in the given equation, the relationship between the independent andDdependent DOFs c