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On the plane contact problem for a frictionless elastic layer

1973; Elsevier BV; Volume: 9; Issue: 8 Linguagem: Inglês

10.1016/0020-7683(73)90021-8

1879-2146

M. Ratwani, F. Erdoğan,

Numerical methods in engineering

The plane contact problem for an elastic layer lying on an elastic half space is considered. A compressive load is applied to the layer through a frictionless rigid stamp. It is assumed that the contact between the layer and the subspace is also frictionless and only compressive normal tractions can be transmitted through the interface. Hence, the width of the contact area along the layer-subspace interface is finite and is unknown. The problem is formulated in terms of a system of singular integral equations in which the unknown functions are the pressure between the stamp and the layer and that between the layer and the subspace. First the problem is solved for the special case of concentrated loads. Two typical stamp geometries, namely, a flat stamp with sharp corners and a curved stamp, are then investigated. In the case of flat stamp the system of integral equations is homogeneous and as a consequence the width of the contact area between the layer and the subspace turns out to be independent of the magnitude of the external load applied to the stamp. In the curved stamp problem, however, the size of this contact region is a function of the magnitude of the external load. Oбc;y;ждa;e;тc;я плo;c;кa;я кo;нтa;ктнa;я зa;дa;khcya; для y;пpy;гo;гo; c;лo;я, лe;жa;щe;гo; нa; y;пpy;гo;м пo;лy;пpo;c;тpa;нc;твe;. Cжимa;e;мa;я нa;гpy;зкa; пpилo;зe;нa; к c;лo;ю пo;c;pe;дc;твo;м жe;c;ткo;гo; штa;мпa;, бe;з y;khcye;тa; тpe;ния. Пo;дpa;зy;мe;вa;e;тc;я, khcyтo; нe;т тpe;ния в кo;нy;a;ктe; c;лo;я c; пo;дпpo;c;тpa;нc;твo;м и тo;лькo; c;жимa;e;мыe; нo;pмa;льныe; тягo;выe; y;c;илия мo;гy;т пe;pe;дa;вa;тьc;я c;квo;зь пo;вe;pчнo;c;ть pa;здe;лa;. Cлe;дo;вa;тe;льнo;, шиpинa; o;блa;c;ти c;o;пpикo;c;нo;вe;ния пo; пo;вe;pчнo;c;ти мe;ждy; c;лo;e;м и пo;дпpo;c;тpa;нc;твo;м кo;нe;khcyнa; и нe;извe;c;тнa;. Фo;pмy;лиpy;e;тc;я зa;дa;khcya; в видe; c;иc;тe;мы c;ингy;ляpныч интe;гpa;льный y;pa;внe;ний, нe;извe;c;тныe; фy;нкции кo;тo;pыч являютc;я дa;влe;ниe;м мe;здy; штa;мпo;м и c;лo;e;м и мe;ждy; c;лo;e;м и пo;дпpo;c;тpa;нc;твo;м. Bпe;pвыe;, pe;шa;e;тc;я зa;дa;khcya; для двy;ч c;пe;циa;льныч c;лy;khcya;e;в c;o;c;pe;дo;тo;khcye;ннo;й нa;гpy;зки. Иc;c;лe;дy;ютc;я, зa;тe;м, двa; типa; гe;o;мe;тpии штa;мпa;, имe;ннo; нлo;c;кий штa;мп c; o;c;тpыми y;глa;ми и иc;кpивлe;нный штa;мп. Для c;лy;khcya;я плo;c;кo;гo; штa;мпa; c;иc;тe;мa; интe;гpa;льныч y;pa;внe;ний o;днo;po;днa;. Bc;лe;дc;твиe; этo;гo;, шиpинa; кo;нтa;ктa; мe;ждy; c;лo;e;м и пo;дпpo;c;тpa;нc;твo;м нe; зa;виc;ит o;т вe;лиkhcyины внe;шнe;й нa;гpy;зки, пpилo;жe;ннo;й к штa;мпy;. Oднa;кo;, для зa;дa;khcyи иc;кpивлe;ннo;гo; штa;мпa; pa;змe;p o;блa;c;ти pa;йo;нa; кo;нтa;ктa; являe;тc;я фy;нкциe;й вe;лиkhcyины внe;шнe;й нa;гpy;зки.