一维弹性杆件旋转问题的加权残值法和伽辽金法.pdf

瀵瑰涓嬪乏鍥炬墍绀洪棶棰橈紝鍙栨潌涓婍饱澶勪竴寰厓锛岄暱涓喉睉肀 锛屽涓嬪彸鍥炬墍绀 鍒 饊仮 (肀 + 肀戫饱) 鈭 饊仮 (肀? 肀戰€仮 饊寑 = = (1) 肀 + 肀戫饱 鈭 肀 肀戫饱 鐢辫儭鍏嬪畾寰嬶紝寰楀埌搴斿姏-搴斿彉鍏崇郴涓猴細 肀戰€仮 砑 = 饊€葛€寑 = 饊€ (2) 肀戫饱 瀵瑰崟鍏冭繘琛屽彈鍔涘垎鏋愶紝寰厓涓ょ鐨勬潌鍐呭姏宸彁渚涘渾鍛ㄨ繍鍔ㄧ殑鍚戝績鍔涳紙瀹氫箟娌挎潌鑳岀閫変腑涓績鐨勬柟鍚戜负 姝ｏ級锛屽嵆锛 [ ( ) ( )] ( ) ( ) 2 砑 肀 + 肀戫饱 鈭 砑 肀 饊€ = 鈭掜紝 饊€错睉肀 肀 + 饊仮 饊寯 绾﹀幓饊€? 肀戫饱鍙暣鐞嗗緱寰楋細 肀戫紟 + 砑 (肀 + 饊仮)饊寯2 = 0 (3) 肀戫饱 灏?3)寮忎唬鍏?1)寮忥紝灏卞彲浠ュ緱鍒颁綅绉诲嚱鏁版弧瓒崇殑寰垎鏂圭▼锛 肀?饊仮 饊€ 肀戫饱2 + 砑 (肀 + 饊仮)饊寯2 = 0 (4) 褰掍竴鍖栨柟绋嬩负锛 饊仮鈥测€ + 饊仮 + 肀 = 0 饊仮 (0) = 0 饊仮鈥 (1) = 0 瑙ｆ瀽瑙ｏ細 sin 肀 饊仮 (肀? = 鈭 肀 cos 1 涓€銆佸姞鏉冩畫鍊兼硶 鑻ヨ 饊仮虄 (肀? = 肀 (饊亷 + 饊亷 肀 + 饊亷 肀 2) (5) 0 1 2 鍒欚€仮虄 (0) = 0 宸茶婊¤冻锛岃€岃浣 饊仮虄 鈥 (1) = 饊亷0 + 2饊亷1 + 3饊亷2 = 0 (6) 鍒欙細 ( ) ( )