By Friedel Hartmann, Peter Jahn
The e-book teaches engineers many new issues a couple of classical subject which without warning is back within the middle of curiosity due to its relevance for finite point research, for the accuracy of computational methods.
It exhibits that effect services play a basic position within the finite point research of constructions and virtually all of linear computational mechanics. It additionally strives so as to add new and demanding insights into sleek structural research and into computational mechanics by means of constructing the critical function of effect capabilities for the numerical research and to put a brand new starting place to the power and variational principles.
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Extra resources for Statics and Influence Functions - from a Modern Perspective
18 Computing the horizontal displacement of a node with Mohr’s equation and with Betti’s theorem, a moments due to the load, b moments of P∗ = 1, c displacement due to the point load P∗ = 1 (= influence function for the horizontal displacement) (a) (b) (c) 33 34 1 Basics (a) (b) Fig. 139) 0 a strong influence function. Both equations return the same value w(x). 140) where the Green’s function G 0 (y, x) provides the virtual forces and strong influence functions are based on Betti’s theorem, Green’s second identity (Fig.
134) In the case of a slanted beam, a rafter, as in Fig. 16, only the part of δw(x) which points in the direction of the traveling load counts. We could apply the principle of virtual displacements also to compute internal forces, for example, the shear force of the beam in Fig. 15c. In this case, we would install a shear hinge at the source point and spread it by one unit apart. But this is the same as if we would apply Betti’s theorem B (w1 , w2 ) = W1,2 − W2,1 = W1,2 = 0 (W2,1 = 0) . 135) 30 Fig.
The engineer calculates the four beam end actions which belong to the unit displacement ϕei (x), see Eq. 50), and places these in column i of the matrix K. In this approach, the ui are displacements and the fi are forces. 170) because at each step d/dx, we divide by the length. 17 Reduction of the Dimension of a Problem In the displacement method of structural analysis, we speak of the degree of kinematic indeterminacy which is the number of unknown nodal displacements. 17 Reduction of the Dimension of a Problem 41 Fig.
Statics and Influence Functions - from a Modern Perspective by Friedel Hartmann, Peter Jahn