The impact of a plane punch on an elastic half-plane |
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| Affiliation: | 1. Laboratory of Strength of Materials (LabSCo), Università IUAV di Venezia, via Torino 153/A, 30172 Venice, Italy;2. Department of Structural and Geotechnical Engineering (DISG), Sapienza University of Rome, via A. Gramsci 53, 00197 Rome, Italy;3. Department of Architecture Construction Conservation (DACC), Università IUAV di Venezia, Dorsoduro 2206, 30123 Venice, Italy;1. Department of Civil, Chemical, Environmental, and Materials Engineering (DICAM), University of Bologna, Viale del Risorgimento 2, Bologna 40136, Italy;2. Department of Architecture, Built Environment and Construction Engineering, Technical University of Milan, Piazza Leonardo Da Vinci, Milan 20133, Italy;1. Centre for Infrastructure Engineering and Safety (CIES), School of Civil and Environmental Engineering, The University of New South Wales (UNSW), Sydney, Australia;2. Centre for Built Infrastructure Research (CBIR), School of Civil and Environmental Engineering, University of Technology, Sydney (UTS), Australia |
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| Abstract: | The transient dynamic contact problem of the impact of a plane absolutely rigid punch on an elastic half-plane is considered. The solution of the integral equation of this problem in terms of the unknown Laplace transform of the contact stresses at the punch base is constructed by a special method of successive approximations. The solution of the transient dynamic contact problem is obtained after applying an inverse Laplace transformation to the solution of the integral equation over the whole time range of the impact process, and the law of the penetration of the punch into the elastic medium is determined from a Volterra-type integrodifferential equation. The conditions for the punch to begin to separate from the elastic half-plane are formulated from the solution obtained, and all the stages of the separation process are investigated in detail. The law of the punch motion on the elastic half-plane and the width of the contact area, which varies during the separation, are then determined from the solution of the Volterra-type integrodifferential equation when an additional condition is satisfied. |
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