[Scienza delle Costruzioni] Problema elastostatico
Riuscite ad aiutarmi con questo esercizio?
Dato il seguente dominio $\beta$:
[jxg]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[/jxg]
individuare le tensioni emergenti sui suoi quattro spigoli sapendo che il campo degli spostamenti è il seguente:
$ { (u_1=3x_2+(4x_1x_2)/a),( u_2=2x_2+(3x_1x_2^2)/a^2 ):} $
e sapendo che il materiale del dominio è ortotropo con matrice elastica:
$ hat(C)= ( ( alpha_1 , lambda , 0 ),( lambda , alpha_2 , 0 ),( 0 , 0 , G ) ) $
Mi chiedevo inoltre se disponevate di dispense o appunti che potessero aiutarmi nella miglior comprensione dell'argomento. Grazie
Dato il seguente dominio $\beta$:
[jxg]eNrtmm2P2kYQgD/Dr1jpvjZgG9sY1bLUJEdVqWqiJI2SL6kMLLCN8SLb3MFF+e+d2TcvnA3X5rWtj+iyMzv7Os/Meg/HP18/++36zaukH7++fvHyl2e/Je5g7MdDLfXjGU+LRdLvxXm6ocmUrzLGyYLBv5Kuck7ceChqwILlS15s0orxPImHtgSV6a5a8wL0qgCqOd9saF6BTpdAueR5VbI7mrhBPDQC9r5IYCwm5qJ0vXiT7tkGhEVSFTsaD2sZa/eJM3Di4V4IBykchHDLFtU6GQVCJQVUrylbratk5Ai9kmC8oRyQEBiRL3ZlEoUwliiJdfBiwfK0oiCSnlIkyzQrKa4NBaFfFUxPVBSFsszTrbYVZZwIL9iK4b6JVbihOwhCp/4J1aJwVaOxM/B9qzLQixzqXnCYO843uj9nEHpjz+pDK1Q7aYutdjmrzCycejexkZJVG2mJbSpamJEsc2Mp69EyS2c006Z7y/ZgjJUJWm92WcXaO4adXPPbvdlKIRj9wdarvlWH0mN5xfIdFw4VA0g3mUGkqBra1kQNYO+UGso0VrJqXVtjWwD2QWNKO2yx5/ygW6ze/Eptn6zeClm1kZbY5obR2y0v1Awrvk2CwcQJvcBQA7GFalGf0WWVPPIGwTiIJl4UjF0ffkfgDawQJjNeVQDJI3cQTZyRE7qe5/vRZByBlaoTdoUIoXAQBJMJ1k+CiRuNAmC0UMEF86xnR3oqYOpwiutQ2ScSWiLWKnkV3it4WZp4E4LyagaZ5uqJg5/pFLtGhahbpOVa7bAoCuWWM0g4VkDWCswCeibxLJ2/XxV8l8s8o8aZqh8zDlQtWUYVhcUcUMXfJgqdoxB0DMgyIR3nJpOcjlMTzEoPEbNNuqLJYDCANCmKkLAIAX9YsyVCBQAvGGbmUmuGlgoVuEqaUczKpQ7rvfI9bALPFq9pUYK5PC9EWha7WqWiJEMKc/q7D+8+vFqzkoCihA2f4yDkNgVFQcHJC3LLqjURJ9H+FcH+Bh8/yiCTZwL2ttnC5m22RtoLca/kPdLqu6Ef+E7khiMvDHy9t7i5gOnIjzyBsYRZ7zX4PC3kIaQKYh1Ds5A4hQnfUIWKEmQFTD+BjsT/avUAkqOBEpoihYhRMElBbiEcjuqMlIobVrJZpofRkozWIp1T3YcUJFBVwd9TCQjEgi32e4ZKyzS5wkCfTh1HW6twR5ZYvsJ65BfrjU5YAGJZcvV48vTx+GnoC+RU3pb5+QobOSLErJwu13v1JMIPNrM2YGjPDhKi2AkrRdc7U3eIfhZ0144Voooae2hDc30Ka4WsL5N8l2WgV8n3z3IJ/sDfasE6G2NJrgbOUogF2GlVkhDsKq5kNZKlUcedjJtPCqC3fEeAM1Ls8hy8QtKcQA+0IDeyE8KXOoK+RPAE0Xg0lgkeE3gXPF3wfNXgwRNKHMXiKFJ3EecHR989iIqqlUsDGUukDibSOz5vSe/4xCUWs+QytJPvA9rRWWhramu4LGpPsVX02dhqbmX1yLO4NeDKJ8djcL8pudjF0eWrVhgyVY1BUz4qmUcmuXcHcIXY4YN6thoa/FpYTBtYDB/Motex2LH4mVhMG1kct7LodSx2LH4xFpvO6OjBLHZndMfiP2YxO6x4btP4/I+mzDhpoRGuVvD4qZ4plXCvKmyvGrdXRe1VJ2P9Dej/Fbep4+vUWein05/gcwb6yHni+E479OIq9n1APwO8qd4BmRnN9yYWic8d85eAdm83uLvB360Ov+/xcy5v9flFpx95/ZLb79+j7/v9XLY77/mzrj/y/QXnH3n/1P0n/u8dwwerTfXfbOVairKqEx0KZiV1hSir3o57iClcydPaaUZUGaUhZQ4tChuInDUS6XZEdkR+IyLnjUR6HZEdkd+IyEUjkaOOyI7Ir0Ak3nDMpabxvv3GbbjguH7rfdv/H9+3T77J6e7bD7hvu+337bQo+K3NIm1Cse3rGRlL8mqs4orUcaUglnH1374WRw5+LvwtaDr9BDa/o2vxSXJsy67NyfUkt9apVRke59b7TCMXCtnmXOo1Afzw73T8Lpd2ufQz5dJlE4rjS7k0bMulYZdLu1z6hXIpGNfvDeLTq3h/XLxzCE6AyYrXSyvOs1mK72KSuDpsafL7y+sX4HAsok7Q/hg6Tcmc42uDd4znjGxpUfI8zdjdHTBrgoLEC1rOC7YVL6lcakbSCriG1najvny71cwrLmEZ84oubC1muQZ1vx/PdiDl4jVxD9xuif1YPr87P+IL2eJJXr6fJTdjqF/B/wuDhCHg[/jxg]
individuare le tensioni emergenti sui suoi quattro spigoli sapendo che il campo degli spostamenti è il seguente:
$ { (u_1=3x_2+(4x_1x_2)/a),( u_2=2x_2+(3x_1x_2^2)/a^2 ):} $
e sapendo che il materiale del dominio è ortotropo con matrice elastica:
$ hat(C)= ( ( alpha_1 , lambda , 0 ),( lambda , alpha_2 , 0 ),( 0 , 0 , G ) ) $
Mi chiedevo inoltre se disponevate di dispense o appunti che potessero aiutarmi nella miglior comprensione dell'argomento. Grazie
Risposte
Credo che dal campo di spostamento tu debba ricavarti le deformazioni e poi sfruttare il legame costitutivo per poter calcolare le tensioni
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