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- https://ukrayinska.libretexts.org/%D0%86%D0%BD%D0%B6%D0%B5%D0%BD%D0%B5%D1%80%D0%BD%D0%B0/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%BE%D0%B1%D1%83%D0%B4%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F/%D0%91%D1%83%D0%B4%D1%96%D0%B2%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0_(Wierzbicki)/02%3A_%D0%9F%D0%BE%D0%BD%D1%8F%D1%82%D1%82%D1%8F_%D1%81%D1%82%D1%80%D0%B5%D1%81%D1%83%2C_%D1%83%D0%B7%D0%B0%D0%B3%D0%B0%D0%BB%D1%8C%D0%BD%D0%B5%D0%BD%D0%B8%D1%85_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B5%D0%BD%D1%8C_%D1%96_%D1%80%D1%96%D0%B2%D0%BD%D0%BE%D0%B2%D0%B0%D0%B3%D0%B8/2.02%3A_%D0%A0%D0%BE%D0%B7%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%B0_%D1%82%D0%B5%D0%BC%D0%B0_-_%D0%9B%D0%BE%D0%BA%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%80%D1%96%D0%B2%D0%BD%D0%BE%D0%B2%D0%B0%D0%B3%D0%B0_%D0%B7_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF%D1%83_%D0%B2%D1%96%D1%80%D1%82%D1%83%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D1%97_%D1%80%D0%BE%D0%B1%D0%BE%D1%82%D0%B812σijδui,j+12σjiδuj,i=σijδui,j \[\sigma_{ij} (\delta u_{i})_{,j} = (\sigma_{ij}\delta u_{i})_{,j} - (\sigma_{ij})_{,j} \...12σijδui,j+12σjiδuj,i=σijδui,j σij(δui),j=(σijδui),j−(σij),jδui ∫VσijδϵijdV=∫V(σijδui)⏟Ai,j\[∫SσijδuinjdS−∫Vσij,jδuidV=∫STiδuidS
- https://ukrayinska.libretexts.org/%D0%86%D0%BD%D0%B6%D0%B5%D0%BD%D0%B5%D1%80%D0%BD%D0%B0/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%BE%D0%B1%D1%83%D0%B4%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%B0%D0%B5%D1%80%D0%BE%D0%BA%D0%BE%D1%81%D0%BC%D1%96%D1%87%D0%BD%D0%B8%D1%85_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%86%D1%96%D0%B9_%D1%82%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D1%80%D1%96%D0%B0%D0%BB%D1%96%D0%B2_(Alderliesten)/03%3A_%D0%90%D0%BD%D0%B0%D0%BB%D1%96%D0%B7_%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE_%D0%BD%D0%B5%D0%B2%D0%B8%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%BE%D1%97_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B8/08%3A_%D0%9F%D1%80%D0%BE%D0%B3%D0%B8%D0%BD%D0%B8_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%86%D1%96%D0%B9-_%D0%A0%D0%BE%D0%B1%D0%BE%D1%82%D0%B0-%D0%95%D0%BD%D0%B5%D1%80%D0%B3%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D1%96_%D0%BC%D0%B5%D1%82%D0%BE%D0%B4%D0%B8/8.01%3A_%D0%92%D1%96%D1%80%D1%82%D1%83%D0%B0%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D0%BC%D0%B5%D1%82%D0%BE%D0%B4_%D1%80%D0%BE%D0%B1%D0%BE%D1%82%D0%B8(1\ математика {кН}\ cdot\ математика {м})\ cdot\ theta_ {D} =\ int_ {0} ^ {L}\ frac {\ mathrm {m} _ {\ тета} M} {E I} d x =\ int_ {0} ^ {7}\ frac {\ ліворуч\ розрив {x} {7} -1\ вправо)\ лівий (70 x-1...(1\ математика {кН}\ cdot\ математика {м})\ cdot\ theta_ {D} =\ int_ {0} ^ {L}\ frac {\ mathrm {m} _ {\ тета} M} {E I} d x =\ int_ {0} ^ {7}\ frac {\ ліворуч\ розрив {x} {7} -1\ вправо)\ лівий (70 x-10 x^ {2}\ праворуч) d x} {E I} +\ int_ {0} ^ {2}\ frac {\ лівий (\ frac {x} {7}\ праворуч) (-70 х) d x} {E I} +\ int_ {2} ^ {4}\ frac {\ ліворуч\ гідророзриву {x} {7} \ праворуч) [-70 x-18 (x-2)] x} {E I}\\
- https://ukrayinska.libretexts.org/%D0%86%D0%BD%D0%B6%D0%B5%D0%BD%D0%B5%D1%80%D0%BD%D0%B0/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%BE%D0%B1%D1%83%D0%B4%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F/%D0%91%D1%83%D0%B4%D1%96%D0%B2%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0_(Wierzbicki)/02%3A_%D0%9F%D0%BE%D0%BD%D1%8F%D1%82%D1%82%D1%8F_%D1%81%D1%82%D1%80%D0%B5%D1%81%D1%83%2C_%D1%83%D0%B7%D0%B0%D0%B3%D0%B0%D0%BB%D1%8C%D0%BD%D0%B5%D0%BD%D0%B8%D1%85_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B5%D0%BD%D1%8C_%D1%96_%D1%80%D1%96%D0%B2%D0%BD%D0%BE%D0%B2%D0%B0%D0%B3%D0%B8/2.05%3A_%D0%92%D0%B8%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%BD%D1%8F_%D1%80%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D0%BD%D1%8F_%D1%80%D1%96%D0%B2%D0%BD%D0%BE%D0%B2%D0%B0%D0%B3%D0%B8_%D0%B4%D0%BB%D1%8F_%D0%BF%D1%83%D1%87%D0%BA%D1%96%D0%B2_%D0%B7_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF%D1%83_%D0%B2%D1%96%D1%80%D1%82%D1%83%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D1%97_%D1%80%D0%BE%D0%B1%D0%BE%D1%82%D0%B8\[\begin{align} \mathrm{LH} &= - \int_{0}^{l} M (\delta w^{\prime})^{\prime} dx + \int_{0}^{l} N \delta u^{\prime} dx \\[4pt] &= - \left( M \delta w^{\prime} |_{0}^{l} - \int_{0}^{l} M^{\prime} \delta...LH=−∫l0M(δw′)′dx+∫l0Nδu′dx=−(Mδw′|l0−∫l0M′δw′dx)+(Nδu|l0−∫l0Nδudx)=−Mδw′|l0+M′δw|l0−∫l0M′′δwdx+Nδu|l0−∫l0N′δudx
- https://ukrayinska.libretexts.org/%D1%84%D1%96%D0%B7%D0%B8%D0%BA%D0%B8/%D0%9A%D0%BB%D0%B0%D1%81%D0%B8%D1%87%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0/%D0%9A%D0%BB%D0%B0%D1%81%D0%B8%D1%87%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0_(Tatum)/09%3A_%D0%9A%D0%BE%D0%BD%D1%81%D0%B5%D1%80%D0%B2%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D1%96_%D1%81%D0%B8%D0%BB%D0%B8/9.03%3A_%D0%92%D1%96%D1%80%D1%82%D1%83%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%80%D0%BE%D0%B1%D0%BE%D1%82%D0%B0У принципі віртуальної роботи ми уявляємо, що діємо на систему таким чином, щоб збільшити одну з координат. Ми запитуємо себе, скільки роботи нам належить зробити над системою, щоб збільшити цю коорди...У принципі віртуальної роботи ми уявляємо, що діємо на систему таким чином, щоб збільшити одну з координат. Ми запитуємо себе, скільки роботи нам належить зробити над системою, щоб збільшити цю координату на невелику суму. Якщо система почне з рівноваги, то ця робота буде дуже маленькою, і, в межі нескінченно малого переміщення, ця «віртуальна робота» буде дорівнює нулю.
- https://ukrayinska.libretexts.org/%D1%84%D1%96%D0%B7%D0%B8%D0%BA%D0%B8/%D0%9A%D0%BB%D0%B0%D1%81%D0%B8%D1%87%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0/%D0%92%D0%B0%D1%80%D1%96%D0%B0%D1%86%D1%96%D0%B9%D0%BD%D1%96_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF%D0%B8_%D0%B2_%D0%BA%D0%BB%D0%B0%D1%81%D0%B8%D1%87%D0%BD%D1%96%D0%B9_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D1%86%D1%96_(Cline)/06%3A_%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%B0/6.03%3A_%D0%A0%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D0%BD%D1%8F_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%B0_%D0%B7_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF%D1%83_%D0%B4'%D0%90%D0%BB%D0%B0%D0%BC%D0%B1%D0%B5%D1%80%D0%B0Принцип віртуальної роботи забезпечує основу для суворого виведення механіки Лагранжа.