By Jan Holnicki-Szulc
The idea of digital distortions presents an effective device which might be used to regard many difficulties that fluctuate from the actual standpoint. the target of this ebook is to offer a common idea of the digital Distortion approach with the mandatory theoretical heritage and numerous its functions to difficulties of structural research and layout. The booklet is focussed extra on theoretical facets of the issues than at the sensible layout of structurÄB. however, a few numerical algorithms mentioned within the booklet has already been constructed as a computational procedure able to unravel a variety of difficulties of structural research.
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Extra resources for Virtual Distortion Method
Example text
As. = 3 cm2 At'" -_. 1. 4 (a) Structure with fractured members (sequence shown). (b) Structure with plastic members (sequence shown). (c) Structure with cable elements. coefficients 0:. 32), After the initial fracture of the element 54 i collapse following elements: 48 (0: 48 progresses =1. 67). Then the structure becomes a mechanism and the catastrophe occurs. 32 = 3788 N. 4a. ; (j • The virtual distortions 45 calculated by the procedure simulate plastic strains generated in the overloaded elements of the structure.
4 and i to point (vi). viii)If the matrix (D 1j - 5 1j becomes a mechanism and ) is singular, the modified structure global collapse of the structure occurs. In that case terminate analysis - STOP. ix) Determine current stresses in the modified structure from Eq. 6) (substituting the auxiliary state of distortions x) Return to point £0,). (i ii). b), which corresponds to The virtual distortions obtained from ~ = 0 this in Eq. (2. 12). equation can be interpreted as gaps between the fractured ends of failed members.
J • The virtual distortions 45 calculated by the procedure simulate plastic strains generated in the overloaded elements of the structure. 3) loaded truss by the structure horizontal forces with increasing intensity is performed assuming (j = (j = 105 MFa. 943P = 4715 N has been u reached. The corresponding sequence of plastic distortions generated in the elements (marked by the bold line in Fig. 2. 00693. 4b. Simulation of Rod-Cable Structures Virtual distortions can be generated compression in such a way that the for all condition (j cables ~ (j = (j under = 0 is satisfied.