Wuhan University of TechnologyChapter10Evaluation of structural-propertymatrices10.1 Elastic properties10.2 Mass properties10.3 Damping properties10.4 External loading10.5Geometricstiffness10.6 Choice of property formulation10-1
10-1 Wuhan University of Technology 10.1 Elastic properties 10.2 Mass properties 10.3 Damping properties 10.4 External loading 10.5 Geometric stiffness 10.6 Choice of property formulation Chapter 10 Evaluation of structural-property matrices
Wuhan Universityof Technology10.1 Elastic propertiesP.=I1P = 1FIGURE10-1Definitionofflexibilityinfluencecoefficients.Thedefinition ofaflexibilityinfluence coefficient isdeflectionofcoordinateiduetounitloadappliedtocoordinatej10-2
10-2 Wuhan University of Technology 10.1 Elastic properties FIGURE 10-1 Definition of flexibility influence coefficients. The definition of a flexibility influence coefficient is
Wuhan Universityof Technology10.1 Elastic propertiesThe deflection at point 1 due to any combination of loads may be expressed asU1=fiiP+fi2Pe+fisPa+..+finPnf12fi3..[Ji1fiNP11f21fo2fosfaNV2P2预fi,f.f.NViPv=fpv=ffs10-3
10-3 Wuhan University of Technology 10.1 Elastic properties The deflection at point 1 due to any combination of loads may be expressed as
Wuhan Universityof Technology10.1 Elastic propertiesThestiffness influencecoefficients inFig.102arenumericallyequal totheapplied forces required to maintain the specified displacement condition. Theyarepositivewhenthesenseof theappliedforcecorrespondstoapositivedisplacementandnegativeotherwise.P,=kup,=kPinD.-2=k2P,=k,Pn=kN2FFIGURE10-2Definitionofstiffnessinfluencecoefficients.10-4
10-4 Wuhan University of Technology 10.1 Elastic properties The stiffness influence coefficients in Fig. 102 are numerically equal to the applied forces required to maintain the specified displacement condition. They are positive when the sense of the applied force corresponds to a positive displacement and negative otherwise. FIGURE 10-2 Definition of stiffness influence coefficients
Wuhan Universityof Technology10.1 Elastic propertiesStrainenergy.Thestrainenergystoredinanystructuremaybeexpressedconvenientlyintermsof eithertheflexibilityorthestiffnessmatrix.ThestrainenergyUisequaltotheworkdoneindistortingthesystem;thusN1ZUP,Ui2i=11Ufpp121vTkvU12Finally,whenitisnotedthatthestrainenergystoredinastablestructureduring any distortion must always be positive, it is evident thatvTkv>0pTfp>0and10-5
10-5 Wuhan University of Technology 10.1 Elastic properties Strain energy . The strain energy stored in any structure may be expressed conveniently in terms of either the flexibility or the stiffness matrix. The strain energy U is equal to the work done in distorting the system; thus Finally, when it is noted that the strain energy stored in a stable structure during any distortion must always be positive, it is evident that