Fall 2001 16.313-1 Introduction Root locus methods have Advantages k Good indicator if transient response k Explicity shows location of all closed-loop poles Trade-offs in the design are fairly clear Disadvantages k Requires a transfer function model(poles and zeros) k Difficult to infer all performance metrics k Hard to determine response to steady-state(sinusoids
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MG!∈R- ORDER5)sT6As RREL丹T(0sHP5 BETWEEN1MER6soN5毛 TAST∈P兵 ND THE POLE LOCAT(0NS心EK ALCULATE0 FoR A SECOND-ORDER SYSTEM GuES60工 NSIGHTS AcTuALLy Gooo APPRoXIMATIONS foR MAwy HIGHER- ORDER SYSTEMS BECAUSE THEIR
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properties of finite dement soltions Noded point equilibrio At a node, the sow of he elemeat nodal forces s in equilibriun with Hhe externed loads
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How many quadrature points do you need to integrate a polynomial of order p= 3 exactly using Gauss'method
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Concept Question How many quadrature points do you need to integrate exactly the stiffness matrix of a lD finite element with quadratic interpolation for the displacements? gauss
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The finite element method(I for three-diwnensional robles Potential enery applied to one eleet
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cmaulenon o isoparametRic elemets (Bathes book Consider the uadriltersd denat shown in the 8oc nodd coordinates
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What do you think the eigenvectors of the element stiff- ness matrix represent? 1. a basis in which the stiffness matrix would be diago- nal (if rotated to that basis) 2. a set of nodal displacements for the element corre-
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Numerical integration Consider He 4-D integral =+(s 1 Seek n-point apploxiwisfions G~2M =1 are the weights and
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How many zero eigenvalues do you think any element stiffness matrix (regardless of the type of finite element nterpolation should have in 2D and 3D, respectively?
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