Vieäc sö� duïng noù daãn ñeán vieäc phaân tích hình hoïc phi tuyeán cuûa keát

Vieäc sö? duïng noù daãn ñeán vieäc phaân

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Treân ñaây laø caùch dieãn taû ñuùng ñaén cuûa bieán daïng baát chaáp caáp cuûa ñoä lôùn cuûa chuyeån vò. Vieäc söû duïng noù daãn ñeán vieäc phaân tích hình hoïc phi tuyeán cuûa keát caáu, ñieàu naøy laøm baøi toaùn raát phöùc taïp. (2.86)
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Giaùo Trình CÔ CHÖÔNG 2: ÖÙNG SUAÁT VAØ BIEÁN DAÏNG 91 TS. Vuõ Coâng Hoøa Trong ña soá caùc aùp duïng thöïc tieãn vaøo keát caáu, moät caùch ñôn giaûn hôïp lyù laø giaû thieát tuyeán tính hình hoïc: gradient cuûa caùc chuyeån vò raát beù: 1 x u i k  Suy ra bình phöông vaø tích soá cuûa chuùng coù theå boû qua. Nhö theá (5.86 ) thaønh: ); x v y u ( 2 1 ; z w ; y v ; x u xy zz yy xx (2.88) ); y w z v ( 2 1 ); x w z u ( 2 1 yz xz (2.89) Ñeå naém vöõng yù nghóa hình hoïc cuûa caùc ñaïi löôïng ij , chæ caàn suy luaän trong moät maët phaúng (x, y), (hình 2.14). Goïi AB vaø AC laø 2 phaàn töû ñöôøng cuûa hình thaùi ban ñaàu, vuoâng goùc vôùi nhau, chuyeån vò ñeán A B vaø A C trong hình thaùi ñaõ bieán daïng. Goïi u, v laø chuyeån vò cuûa A theo phöông x, y ; 1 , 2 laø goùc quay cuûa AB so vôùi x vaø AC so vôùi truïc y. Hình 2.14 xx ' ' x u dx dx x u AB AB B A (2.90) yy ' ' y v dy dy y u AC AC C A (2.91) Vì: dy dx x y x y dy y u u dy y v v dx x v v ' dx u x y ' B ' A A B ' C C ' dy dx x u u
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Giaùo Trình CÔ CHÖÔNG 2: ÖÙNG SUAÁT VAØ BIEÁN DAÏNG 92 TS. Vuõ Coâng Hoøa x v dx v dx . x v v tg ' 1 x (2.92) y u dy u dy . y u u tg ' 2 y (2.93) 1 , y x  (2.94) dx ) x u 1 ( dx dx ' (2.95) dy ) y v 1 ( dy dy ' (2.96) Bieán daïng goùc vuoâng: xy xy . 2 x v y u (2.97) Töông töï: xz xz . 2 x w z u (2.98) yz yz . 2 y w z v (2.99) coøn goïi laø goùc tröôït neân caùc thaønh phaàn (2.97), (2.98), (2.99) coøn goïi laø bieán daïng tröôït. Coøn xx , yy , zz : bieán daïng phaùp (bieán daïng daøi). Tensor coøn coù theå dieãn taû döôùi daïng: zz yz yy xz xy xx ñx 2 1 2 1 2 1 T (2.100)
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Giaùo Trình CÔ CHÖÔNG 2: ÖÙNG SUAÁT VAØ BIEÁN DAÏNG 93 TS. Vuõ Coâng Hoøa 4.3. Quan heä giöõa öùng suaát vaø bieán daïng: Ñoái vôùi vaät lieäu ñoàng chaát vaø ñaúng höôùng, Hooke ñaõ tìm ra moái quan heä giöõa öùng suaát vaø bieán daïng (coøn goïi laø ñònh luaät Hooke): Ta coù: E: Modulus ñaøn hoài cuûa vaät lieäu, [löïc/ bình phöông chieàu daøi). Noù tuøy thuoäc vaøo vaät lieäu vaø laø haèng soá cho moãi vaät lieäu.
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