The 24 reference contexts in paper G. Kuvyrkin N., V. Zarubin S., В. Зарубин С., Г. Кувыркин Н. (2016) “Оценки упругих свойств композита с анизотропными шаровыми включениями // Estimating of the Elastic Properties of the Composite with Anisotropic Ball Inclusions” / spz:neicon:technomag:y:2014:i:8:p:237-255

  1. Start
    1536
    Prefix
    Î ̨ ̃‚ ̊ ÒÎÓ‚‡:ÍÓÏÔÓÁËÚ; ‡ÌËÁÓÚÓÔÌ ̊ ̄‡Ó‚ ̊ ‚ÍÎ ̨ ̃ÂÌˡ; ÛÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË. ¬‚‰ÂÌË »Á‚ÂÒÚÌÓ ÌÂÒÍÓÎ ̧ÍÓ ÔÓ‰ıÓ‰Ó‚ Í ÓˆÂÌÍ ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡ ÔÓ ËÁ‚ÂÒÚÌ ̊Ï Ò‚ÓÈÒÚ‚‡Ï Â„Ó Ï‡Úˈ ̊ Ë ‡ÏËÛ ̨ ̆Ëı ‚ÍÎ ̨ ̃ÂÌËÈ ÔË Á‡‰‡ÌÌÓÈ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ
    Exact
    [1,2,3,4,5,6,7,8,9]
    Suffix
    . ›ÚË ÔÓ‰ıÓ‰ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔÓÎÛ ̃ËÎË ‡Á‚ËÚË ‚ ‡·ÓÚ‡ı ÓÚ ̃ÂÒÚ‚ÂÌÌ ̊ı Ë Á‡Û·ÂÊÌ ̊ı ËÒÒΉӂ‡ÚÂÎÂÈ [10,11,12,13,14,15,16,17,18] Ë · ̊ÎË ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ̇ ÏÂÚÓ‰ ̊ ÔÓ„ÌÓÁËÓ‚‡Ìˡ ÚÂÔÎÓÙËÁË ̃ÂÒÍËı Ë ̋ÎÂÍÚÓχ„ÌËÚÌ ̊ı Ò‚ÓÈÒÚ‚ χÚÂˇÎÓ‚ [19,20,21,22,23,24], ‡ Ú‡ÍÊ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ÔË ÓÔËÒ‡ÌËË Ôӂ‰ÂÌˡ χÚÂˇÎÓ‚ ÔË ÍÓÏ·ËÌËÓ‚‡ÌÌ ̊ı ‚ÓÁ‰ÂÈÒڂˡı (̇ÔËÏÂ, ÔË ÔÓÒÚÓÂÌËË Ï‡ÚÂχÚË ̃ÂÒÍËı ÏÓ
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  2. Start
    1661
    Prefix
    ¬‚‰ÂÌË »Á‚ÂÒÚÌÓ ÌÂÒÍÓÎ ̧ÍÓ ÔÓ‰ıÓ‰Ó‚ Í ÓˆÂÌÍ ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡ ÔÓ ËÁ‚ÂÒÚÌ ̊Ï Ò‚ÓÈÒÚ‚‡Ï Â„Ó Ï‡Úˈ ̊ Ë ‡ÏËÛ ̨ ̆Ëı ‚ÍÎ ̨ ̃ÂÌËÈ ÔË Á‡‰‡ÌÌÓÈ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ [1,2,3,4,5,6,7,8,9]. ›ÚË ÔÓ‰ıÓ‰ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔÓÎÛ ̃ËÎË ‡Á‚ËÚË ‚ ‡·ÓÚ‡ı ÓÚ ̃ÂÒÚ‚ÂÌÌ ̊ı Ë Á‡Û·ÂÊÌ ̊ı ËÒÒΉӂ‡ÚÂÎÂÈ
    Exact
    [10,11,12,13,14,15,16,17,18]
    Suffix
    Ë · ̊ÎË ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ̇ ÏÂÚÓ‰ ̊ ÔÓ„ÌÓÁËÓ‚‡Ìˡ ÚÂÔÎÓÙËÁË ̃ÂÒÍËı Ë ̋ÎÂÍÚÓχ„ÌËÚÌ ̊ı Ò‚ÓÈÒÚ‚ χÚÂˇÎÓ‚ [19,20,21,22,23,24], ‡ Ú‡ÍÊ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ÔË ÓÔËÒ‡ÌËË Ôӂ‰ÂÌˡ χÚÂˇÎÓ‚ ÔË ÍÓÏ·ËÌËÓ‚‡ÌÌ ̊ı ‚ÓÁ‰ÂÈÒڂˡı (̇ÔËÏÂ, ÔË ÔÓÒÚÓÂÌËË Ï‡ÚÂχÚË ̃ÂÒÍËı ÏÓ‰ÂÎÂÈ ÚÂÏÓÛÔÛ„ÓÒÚË, ̋ÎÂÍÚÓ- Ë Ï‡„ÌËÚÓÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚÓ‚ [25,26,27].
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  3. Start
    1796
    Prefix
    ›ÚË ÔÓ‰ıÓ‰ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔÓÎÛ ̃ËÎË ‡Á‚ËÚË ‚ ‡·ÓÚ‡ı ÓÚ ̃ÂÒÚ‚ÂÌÌ ̊ı Ë Á‡Û·ÂÊÌ ̊ı ËÒÒΉӂ‡ÚÂÎÂÈ [10,11,12,13,14,15,16,17,18] Ë · ̊ÎË ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ̇ ÏÂÚÓ‰ ̊ ÔÓ„ÌÓÁËÓ‚‡Ìˡ ÚÂÔÎÓÙËÁË ̃ÂÒÍËı Ë ̋ÎÂÍÚÓχ„ÌËÚÌ ̊ı Ò‚ÓÈÒÚ‚ χÚÂˇÎÓ‚
    Exact
    [19,20,21,22,23,24]
    Suffix
    , ‡ Ú‡ÍÊ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ÔË ÓÔËÒ‡ÌËË Ôӂ‰ÂÌˡ χÚÂˇÎÓ‚ ÔË ÍÓÏ·ËÌËÓ‚‡ÌÌ ̊ı ‚ÓÁ‰ÂÈÒڂˡı (̇ÔËÏÂ, ÔË ÔÓÒÚÓÂÌËË Ï‡ÚÂχÚË ̃ÂÒÍËı ÏÓ‰ÂÎÂÈ ÚÂÏÓÛÔÛ„ÓÒÚË, ̋ÎÂÍÚÓ- Ë Ï‡„ÌËÚÓÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚÓ‚ [25,26,27].
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  4. Start
    2012
    Prefix
    ̃ÂÒÚ‚ÂÌÌ ̊ı Ë Á‡Û·ÂÊÌ ̊ı ËÒÒΉӂ‡ÚÂÎÂÈ [10,11,12,13,14,15,16,17,18] Ë · ̊ÎË ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ̇ ÏÂÚÓ‰ ̊ ÔÓ„ÌÓÁËÓ‚‡Ìˡ ÚÂÔÎÓÙËÁË ̃ÂÒÍËı Ë ̋ÎÂÍÚÓχ„ÌËÚÌ ̊ı Ò‚ÓÈÒÚ‚ χÚÂˇÎÓ‚ [19,20,21,22,23,24], ‡ Ú‡ÍÊ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ÔË ÓÔËÒ‡ÌËË Ôӂ‰ÂÌˡ χÚÂˇÎÓ‚ ÔË ÍÓÏ·ËÌËÓ‚‡ÌÌ ̊ı ‚ÓÁ‰ÂÈÒڂˡı (̇ÔËÏÂ, ÔË ÔÓÒÚÓÂÌËË Ï‡ÚÂχÚË ̃ÂÒÍËı ÏÓ‰ÂÎÂÈ ÚÂÏÓÛÔÛ„ÓÒÚË, ̋ÎÂÍÚÓ- Ë Ï‡„ÌËÚÓÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚÓ‚
    Exact
    [25,26,27]
    Suffix
    . Õ‡ˇ‰Û Ò ÍÓÏÔÓÁËÚ‡ÏË, ‡ÏËÓ‚‡ÌÌ ̊ÏË ‚ÓÎÓÍÌËÒÚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË, ̄ËÓÍÓ ËÒÔÓÎ ̧ÁÛ ̨Ú ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ ÍÓÏÔÓÁËÚ ̊, ‚ ÍÓÚÓ ̊ı ‚ ͇ ̃ÂÒÚ‚Â ‚ÍÎ ̨ ̃ÂÌËÈ ÔËÏÂÌˇ ̨Ú ̃‡ÒÚˈ ̊ ËÁ ‚ ̊ÒÓÍÓÔÓ ̃Ì ̊ı Ë ‚ ̊ÒÓÍÓÏÓ‰ÛÎ ̧Ì ̊ı χÚÂˇÎÓ‚, ‚ ÚÓÏ ̃ËÒΠ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊ [28,29,30,31].
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  5. Start
    2297
    Prefix
    Õ‡ˇ‰Û Ò ÍÓÏÔÓÁËÚ‡ÏË, ‡ÏËÓ‚‡ÌÌ ̊ÏË ‚ÓÎÓÍÌËÒÚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË, ̄ËÓÍÓ ËÒÔÓÎ ̧ÁÛ ̨Ú ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ ÍÓÏÔÓÁËÚ ̊, ‚ ÍÓÚÓ ̊ı ‚ ͇ ̃ÂÒÚ‚Â ‚ÍÎ ̨ ̃ÂÌËÈ ÔËÏÂÌˇ ̨Ú ̃‡ÒÚˈ ̊ ËÁ ‚ ̊ÒÓÍÓÔÓ ̃Ì ̊ı Ë ‚ ̊ÒÓÍÓÏÓ‰ÛÎ ̧Ì ̊ı χÚÂˇÎÓ‚, ‚ ÚÓÏ ̃ËÒΠ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊
    Exact
    [28,29,30,31]
    Suffix
    . ¬ ·ÓÎ ̧ ̄ËÌÒÚ‚Â ÒÎÛ ̃‡Â‚ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı. œÓ ̋ÚÓÏÛ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ó· ̊ ̃ÌÓ ÔËÌËχ ̨Ú ̄‡Ó‚ÓÈ [32,33,34]. ÿËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [35], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊.
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  6. Start
    2528
    Prefix
    , ̄ËÓÍÓ ËÒÔÓÎ ̧ÁÛ ̨Ú ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ ÍÓÏÔÓÁËÚ ̊, ‚ ÍÓÚÓ ̊ı ‚ ͇ ̃ÂÒÚ‚Â ‚ÍÎ ̨ ̃ÂÌËÈ ÔËÏÂÌˇ ̨Ú ̃‡ÒÚˈ ̊ ËÁ ‚ ̊ÒÓÍÓÔÓ ̃Ì ̊ı Ë ‚ ̊ÒÓÍÓÏÓ‰ÛÎ ̧Ì ̊ı χÚÂˇÎÓ‚, ‚ ÚÓÏ ̃ËÒΠ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊ [28,29,30,31]. ¬ ·ÓÎ ̧ ̄ËÌÒÚ‚Â ÒÎÛ ̃‡Â‚ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı. œÓ ̋ÚÓÏÛ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ó· ̊ ̃ÌÓ ÔËÌËχ ̨Ú ̄‡Ó‚ÓÈ
    Exact
    [32,33,34]
    Suffix
    . ÿËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [35], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊. ¬ ͇ ̃ÂÒÚ‚Â Ú‡ÍËı ̃‡ÒÚˈ ̇ıÓ‰ˇÚ ÔËÏÂÌÂÌË ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [36,37,38].
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  7. Start
    2605
    Prefix
    ¬ ·ÓÎ ̧ ̄ËÌÒÚ‚Â ÒÎÛ ̃‡Â‚ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı. œÓ ̋ÚÓÏÛ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ó· ̊ ̃ÌÓ ÔËÌËχ ̨Ú ̄‡Ó‚ÓÈ [32,33,34]. ÿËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË
    Exact
    [35]
    Suffix
    , ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊. ¬ ͇ ̃ÂÒÚ‚Â Ú‡ÍËı ̃‡ÒÚˈ ̇ıÓ‰ˇÚ ÔËÏÂÌÂÌË ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊ [36,37,38]. «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ı ÍÓÏÔÓÁËÚÓ‚ ҂ˉÂÚÂÎ ̧ÒÚ‚ÛÂÚ Ó· ‡ÍÚۇΠ̧ÌÓÒÚË ËÒÒΉӂ‡ÌËÈ ‚ ‰‡ÌÌÓÏ Ì‡Ô‡‚ÎÂÌËË. ̋ÚÓÏÛ Ì‡Ô‡‚ÎÂÌË ̨ ÔËÏ ͇̊ ̨Ú Ë ‡·ÓÚ ̊, ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ӈÂÌÍ ÛÔÛ„Ëı Ò‚ÓÈÒÚ
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  8. Start
    2739
    Prefix
    ¬ ·ÓÎ ̧ ̄ËÌÒÚ‚Â ÒÎÛ ̃‡Â‚ ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı. œÓ ̋ÚÓÏÛ ÙÓÏÛ Ú‡ÍËı ̃‡ÒÚˈ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ó· ̊ ̃ÌÓ ÔËÌËχ ̨Ú ̄‡Ó‚ÓÈ [32,33,34]. ÿËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌ ̊ ÍÓÏÔÓÁËÚ ̊, ̇Á ̊‚‡ÂÏ ̊ ÒÙÂÓÔ·ÒÚË͇ÏË [35], ÍÓÚÓ ̊ ÒÓ‰ÂÊ‡Ú ‰ËÒÔÂÒÌ ̊ ̃‡ÒÚˈ ̊ ÒÚÓ„Ó ̄‡Ó‚ÓÈ ÙÓÏ ̊. ¬ ͇ ̃ÂÒÚ‚Â Ú‡ÍËı ̃‡ÒÚˈ ̇ıÓ‰ˇÚ ÔËÏÂÌÂÌË ÔÓÎ ̊ ÒÚÂÍÎÓÒÙÂ ̊
    Exact
    [36,37,38]
    Suffix
    . «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ı ÍÓÏÔÓÁËÚÓ‚ ҂ˉÂÚÂÎ ̧ÒÚ‚ÛÂÚ Ó· ‡ÍÚۇΠ̧ÌÓÒÚË ËÒÒΉӂ‡ÌËÈ ‚ ‰‡ÌÌÓÏ Ì‡Ô‡‚ÎÂÌËË. ̋ÚÓÏÛ Ì‡Ô‡‚ÎÂÌË ̨ ÔËÏ ͇̊ ̨Ú Ë ‡·ÓÚ ̊, ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ӈÂÌÍ ÛÔÛ„Ëı Ò‚ÓÈÒÚ‚ ÔÓËÒÚ ̊ı ÏÂÚ‡ÎÎÓ‚, ÏÂÚ‡ÎÎÓÍÂ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚ [39,40,41, 42,43,44,45,46], ÔÓÒÍÓÎ ̧ÍÛ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÛ ̨ ÔÓÛ ‰Ó
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  9. Start
    3083
    Prefix
    «Ì‡ ̃ËÚÂÎ ̧ÌÓ ̃ËÒÎÓ ÔÛ·ÎËÍÛÂÏ ̊ı ‡·ÓÚ ÔÓ ÓˆÂÌÍ ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ı ÍÓÏÔÓÁËÚÓ‚ ҂ˉÂÚÂÎ ̧ÒÚ‚ÛÂÚ Ó· ‡ÍÚۇΠ̧ÌÓÒÚË ËÒÒΉӂ‡ÌËÈ ‚ ‰‡ÌÌÓÏ Ì‡Ô‡‚ÎÂÌËË. ̋ÚÓÏÛ Ì‡Ô‡‚ÎÂÌË ̨ ÔËÏ ͇̊ ̨Ú Ë ‡·ÓÚ ̊, ÔÓÒ‚ˇ ̆ÂÌÌ ̊ ӈÂÌÍ ÛÔÛ„Ëı Ò‚ÓÈÒÚ‚ ÔÓËÒÚ ̊ı ÏÂÚ‡ÎÎÓ‚, ÏÂÚ‡ÎÎÓÍÂ‡ÏËÍË, ÔÓÎËÏÂÓ‚ Ë ÒÚÓËÚÂÎ ̧Ì ̊ı χÚÂˇÎÓ‚
    Exact
    [39,40,41, 42,43,44,45,46]
    Suffix
    , ÔÓÒÍÓÎ ̧ÍÛ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÛ ̨ ÔÓÛ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ‡·ÒÓÎ ̨ÚÌÓ ÔÓ‰‡ÚÎË‚Ó ‚ÍÎ ̨ ̃ÂÌËÂ. ¬ ·ÓÎ ̧ ̄ËÌÒÚ‚Â ÓÔÛ·ÎËÍÓ‚‡ÌÌ ̊ı ‡·ÓÚ, ÔÓÒ‚ˇ ̆ÂÌÌ ̊ı ËÒÒΉӂ‡ÌË ̨ ÛÔÛ„Ëı Ò‚ÓÈÒÚ‚ ‰ËÒÔÂÒÌÓ ÛÔÓ ̃ÌÂÌÌ ̊ı ÍÓÏÔÓÁËÚÓ‚, χÚˈ‡ ÍÓÏÔÓÁËÚ‡ Ë ‚ÍÎ ̨ ̃ÂÌˡ Ò ̃ËÚ‡ ̨Ú ËÁÓÚÓÔÌ ̊ÏË.
    (check this in PDF content)

  10. Start
    3803
    Prefix
    ≈ÒÎË ‚Ò ‚ÍÎ ̨ ̃ÂÌˡ Ó‰Ë̇ÍÓ‚Ó„Ó ‡ÁÏÂ‡, ÚÓ ÔË Ëı ̇˷ÓΠÔÎÓÚÌÓÈ ÛÔ‡ÍÓ‚ÍÂ, ÍÓ„‰‡ ‚ ͇ʉÓÏ ÒÎÓ ˆÂÌÚ ̊ ÍÓÌÚ‡ÍÚËÛ ̨ ̆Ëı ÏÂÊ‰Û ÒÓ·ÓÈ ̄‡Ó‚ ̇ıÓ‰ˇÚÒˇ ‚ ‚Â ̄Ë̇ı Ô‡‚ËÎ ̧Ì ̊ı ÚÂÛ„ÓÎ ̧ÌËÍÓ‚, Ó· ̇ÂÏ̇ˇ ÍÓ̈ÂÌÚ‡ˆËˇCV ̄‡Ó‚ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ ÔËÌËχÂÚ Ì‡Ë·ÓÎ ̧ ̄ Á̇ ̃ÂÌËÂC◦V=π/(3 √ 2)≈0,7405
    Exact
    [47]
    Suffix
    . ≈ÒÎË ÌÂ Û ̃ËÚ ̊‚‡Ú ̧ ÍÓÌÍÂÚÌ ̊È ‡ÁÏÂ ‚ÍÎ ̨ ̃ÂÌËÈ Ë Ò ̃ËÚ‡Ú ̧, ̃ÚÓ Ëı ‰Ë‡ÏÂÚ ÏÓÊÂÚ ÔËÌËÏ‡Ú ̧ Á̇ ̃ÂÌˡ ÓÚ ÌÂÍÓÚÓÓ„Ó ÍÓÌ ̃ÌÓ„Ó ‰Ó ·ÂÒÍÓÌ ̃ÌÓ Ï‡ÎÓ„Ó, Ú.Â. ‚ÓÁÏÓÊÌÓ Á‡ÔÓÎÌÂÌË ‚ÒÂı ÔÛÒÚÓÚ ÏÂÊ‰Û ÍÛÔÌ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË, ÚÓ ‰ÓÔÛÒÚËÏÓ ‡ÒÒχÚË‚‡Ú ̧ Á̇ ̃ÂÌˡCV∈[0,1]. œËÏÂÏ ËÁ‚ÂÒÚÌ ̊ÏË Ó· ̇ÂÏÌ ̊È ÏÓ‰ÛÎ ̧K◦Ë ÏÓ‰ÛÎ ̧ Ò‰‚Ë„‡G◦ËÁÓÚÓÔÌÓÈ Ï‡Úˈ ̊ Ë ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C•ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË ‡
    (check this in PDF content)

  11. Start
    4560
    Prefix
    –‡ÒÔÓÎÓÊÂÌË ‚ÍÎ ̨ ̃ÂÌËÈ ÔÓÎÓÊËÏ ÒÎÛ ̃‡ÈÌ ̊Ï, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ Ò ̃ËÚ‡Ú ̧ ÍÓÏÔÓÁËÚ Ï‡ÍÓÒÍÓÔË ̃ÂÒÍË ËÁÓÚÓÔÌ ̊Ï, ÓˆÂÌË‚‡ÂÏ ̊ ÛÔÛ„Ë ҂ÓÈÒÚ‚‡ ÍÓÚÓÓ„Ó ÓÔ‰ÂÎËÏ Ó· ̇ÂÏÌ ̊Ï ÏÓ‰ÛÎÂÏKË ÏÓ‰ÛÎÂÏ Ò‰‚Ë„‡G. ◊ÂÂÁ ̋ÚË ÏÓ‰ÛÎË ÏÓÊÌÓ ‚ ̊‡ÁËÚ ̧ ÔÓ‰ÓÎ ̧Ì ̊È ÏÓ‰ÛÎ ̧ ÛÔÛ„ÓÒÚË (ÏÓ‰ÛÎ ̧ fiÌ„‡) E= 9KG 3K+G Ë ÍÓ ̋ÙÙˈËÂÌÚ œÛ‡ÒÒÓ̇ν= 1 2 − 3G 6K+ 2G ÍÓÏÔÓÁËÚ‡
    Exact
    [48]
    Suffix
    . 1. ŒÒÌÓ‚Ì ̊ ÒÓÓÚÌÓ ̄ÂÌˡ ”ÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË ËÁÓÚÓÔÌ ̊ı ÍÓÏÔÓÁËÚ‡ ‚ ˆÂÎÓÏ Ë Â„Ó Ï‡Úˈ ̊ ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ Ó‰Ë̇ÍÓ‚ÓÈ ÚÂÌÁÓÌÓÈ ÙÓÏ [6] (̇ ÔËÏÂ ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡) Ĉ= 3K̂V+ 2ĜD,̂S=1 3K V̂+1 2G D̂,(1) „‰Â̂CË̂S| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË Ë ÔÓ‰‡ÚÎË‚ÓÒÚË ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ, ‡̂VË̂D| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡, ˇ‚Ρ ̨ ̆ËÂÒˇ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ó· ̇ÂÏÌÓÈ Ë ‰Â‚ˇÚÓ
    (check this in PDF content)

  12. Start
    4707
    Prefix
    ◊ÂÂÁ ̋ÚË ÏÓ‰ÛÎË ÏÓÊÌÓ ‚ ̊‡ÁËÚ ̧ ÔÓ‰ÓÎ ̧Ì ̊È ÏÓ‰ÛÎ ̧ ÛÔÛ„ÓÒÚË (ÏÓ‰ÛÎ ̧ fiÌ„‡) E= 9KG 3K+G Ë ÍÓ ̋ÙÙˈËÂÌÚ œÛ‡ÒÒÓ̇ν= 1 2 − 3G 6K+ 2G ÍÓÏÔÓÁËÚ‡ [48]. 1. ŒÒÌÓ‚Ì ̊ ÒÓÓÚÌÓ ̄ÂÌˡ ”ÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË ËÁÓÚÓÔÌ ̊ı ÍÓÏÔÓÁËÚ‡ ‚ ˆÂÎÓÏ Ë Â„Ó Ï‡Úˈ ̊ ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ Ó‰Ë̇ÍÓ‚ÓÈ ÚÂÌÁÓÌÓÈ ÙÓÏÂ
    Exact
    [6]
    Suffix
    (̇ ÔËÏÂ ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡) Ĉ= 3K̂V+ 2ĜD,̂S=1 3K V̂+1 2G D̂,(1) „‰Â̂CË̂S| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË Ë ÔÓ‰‡ÚÎË‚ÓÒÚË ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ, ‡̂VË̂D| ÚÂÌÁÓ ̊ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡, ˇ‚Ρ ̨ ̆ËÂÒˇ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ó· ̇ÂÏÌÓÈ Ë ‰Â‚ˇÚÓÌÓÈ ÒÓÒÚ‡‚Ρ ̨ ̆ËÏË Â‰ËÌË ̃ÌÓ„Ó ÚÂÌÁÓ‡ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡̂I=̂V+̂D.
    (check this in PDF content)

  13. Start
    5480
    Prefix
    ̧ ‰ËÌË ̃Ì ̊È ÚÂÌÁÓ ‚ÚÓÓ„Ó ‡Ì„‡ Ò ÍÓÏÔÓÌÂÌÚ‡ÏËδij,i, j= 1,2,3(δij= 1ÔË i=jËδij= 0ÔËi6=j), ÚÓ ÍÓÏÔÓÌÂÌÚ ̊ ̋ÚËı ÒÓÒÚ‡‚Ρ ̨ ̆Ëı ÔËÏÛÚ ‚ˉ Vijmn= δijδmn 3 , Dijmn=Iijmn−Vijmn, m, n= 1,2,3, „‰ÂIklmn= (δkmδln+δknδlm)/2| ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂I. — Û ̃ÂÚÓÏ ̋ÚËı ÙÓÏÛÎ, Ô‡‚Ë· ÒÛÏÏËÓ‚‡Ìˡ Ò·„‡ÂÏ ̊ı ÔÓ ÔÓ‚ÚÓˇ ̨ ̆ËÏÒˇ ‚ ÒÓÏÌÓÊËÚÂΡı ·ÚËÌÒÍËı Ë̉ÂÍÒ‡ı Ë ‡‚ÂÌÒÚ‚‡ δii= 3ÏÓÊÌÓ ÛÒÚ‡ÌÓ‚ËÚ ̧, ̃ÚÓ
    Exact
    [6]
    Suffix
    VijmnVmnkl=Vijkl,DijmnDmnkl=DijklËVijmnDmnkl= 0, k, l= 1,2,3, Ú.Â. V̂··̂V=̂V,̂D··̂D=̂D,̂V··̂D=̂O4,(2) „‰Â̂O4| ÚÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ Ò ÌÛ΂ ̊ÏË ÍÓÏÔÓÌÂÌÚ‡ÏË, ‡ ͇ʉ‡ˇ ËÁ ÚÓ ̃ÂÍ ÏÂÊ‰Û ÒÓÏÌÓÊËÚÂΡÏË ‚ ÔÓËÁ‚‰ÂÌËË ÚÂÌÁÓÓ‚ ÓÁ̇ ̃‡ÂÚ Ò‚ÂÚ ̊‚‡ÌË ÔÓ Ë̉ÂÍÒÛ, Ó‰Ë̇ÍÓ‚ÓÏÛ ‚ Ó·ÓËı ÒÓÏÌÓÊËÚÂΡı [49].
    (check this in PDF content)

  14. Start
    5770
    Prefix
    V̂··̂V=̂V,̂D··̂D=̂D,̂V··̂D=̂O4,(2) „‰Â̂O4| ÚÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ Ò ÌÛ΂ ̊ÏË ÍÓÏÔÓÌÂÌÚ‡ÏË, ‡ ͇ʉ‡ˇ ËÁ ÚÓ ̃ÂÍ ÏÂÊ‰Û ÒÓÏÌÓÊËÚÂΡÏË ‚ ÔÓËÁ‚‰ÂÌËË ÚÂÌÁÓÓ‚ ÓÁ̇ ̃‡ÂÚ Ò‚ÂÚ ̊‚‡ÌË ÔÓ Ë̉ÂÍÒÛ, Ó‰Ë̇ÍÓ‚ÓÏÛ ‚ Ó·ÓËı ÒÓÏÌÓÊËÚÂΡı
    Exact
    [49]
    Suffix
    . “ÂÌÁÓ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ËÏÂÂÚ ‰‚‡ ÎËÌÂÈÌ ̊ı ÓÚÌÓÒËÚÂÎ ̧ÌÓ Ò‚ÓËı ÍÓÏÔÓÌÂÌÚ ËÌ‚‡ˇÌÚ‡, ÔÓÎÛ ̃‡ÂÏ ̊ı Ò‚ÂÚ ̊‚‡ÌËÂÏ ÔÓ ‰‚ÛÏ Ô‡‡Ï Ë̉ÂÍÒÓ‚. ƒÎˇ ÚÂÌÁÓ‡, ÓÔ‰ÂΡÂÏÓ„Ó ÔÂ‚ ̊Ï ‡‚ÂÌÒÚ‚ÓÏ (1), ̋ÚË ËÌ‚‡ˇÌÚ ̊ ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ ‚ˉ Ĉ·· ··̂V=Ciimm= 9K,̂C·· ··̂D=Cimim−Ciimm 3 = 10G,(3) ‡ ‰Îˇ ÚÂÌÁÓ‡, ÓÔ‰ÂΡÂÏÓ„Ó ‚ÚÓ ̊Ï ‡‚ÂÌÒÚ‚ÓÏ (1) | Ŝ·· ··̂V=Siimm=1 K ,̂S·· ··̂D=Simim− Siimm 3 = 5 2G .(4)
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  15. Start
    6649
    Prefix
    ŒÒ‰ÌÂÌÌ ̊ ÔÓ Ó· ̇ÂÏÛV0ÎÓ͇Π̧Ì ̊ Á̇ ̃ÂÌˡˆs(M)ˈe(M)ÚÂÌÁÓÓ‚ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ì‡ÔˇÊÂÌËÈ Ë ‰ÂÙÓχˆËË ‚ ÓÍÂÒÚÌÓÒÚË ÚÓ ̃ÍËM∈V0ËÏ ̨Ú ‚ˉ 〈ˆs〉= 1 V0 ∫ V0 ˆs(M)dV(M)или〈ˆe〉= 1 V0 ∫ V0 ˆe(M)dV(M), „‰Â Û„ÎÓ‚ ̊ ÒÍÓ·ÍË Ó·ÓÁ̇ ̃‡ ̨Ú ÓÔÂ‡ˆË ̨ ÓÒ‰ÌÂÌˡ. ÃÓ‰ÛÎË ÛÔÛ„ÓÒÚË ÍÓÏÔÓÁËÚ‡, Ò‚ˇÁ ̊‚‡ ̨ ̆Ë ̋ÚË ÓÒ‰ÌÂÌÌ ̊ ÚÂÌÁÓ ̊, ̇Á ̊‚‡ ̨Ú ̋ÙÙÂÍÚË‚Ì ̊ÏË
    Exact
    [49]
    Suffix
    . ¬‚‰ÂÏ ̋ÚË ÏÓ‰ÛÎË ËÁ ÛÒÎӂˡ ‡‚ÂÌÒÚ‚‡ Ó· ̇ÂÏÌÓÈ ÔÎÓÚÌÓÒÚË ÔÓÚÂ̈ˇΠ̧ÌÓÈ ̋ÌÂ„ËË ‰ÂÙÓχˆËË ‚ ËÁÓÚÓÔÌÓÈ ÒÂ‰Â Ë ‚ ‡Π̧ÌÓÏ ÍÓÏÔÓÁËÚÂ: 1 2 〈ˆe〉 ··̂C·· 〈ˆe〉= 1 2 〈ˆs〉 ··̂S·· 〈ˆs〉= 1 2V0 ∫ V0 ˆs∗(M)··ˆe∗(M)dV(M) = = 1 2V0 ∫ V0 C∗ijmn(M)ε∗mn(M)ε∗ij(M)dV(M)= 1 2V0 ∫ V0 S∗ijmn(M)σ∗mn(M)σ∗ij(M)dV(M),(5) „‰Âˆs∗ˈe∗| ÚÂÌÁÓ ̊ ̇ÔˇÊÂÌËÈ Ë ‰ÂÙÓχˆËË Ò ÍÓÏÔÓÌÂÌÚ‡ÏË ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓσ∗ijËε∗ij, ÓÔ‰ÂÎÂÌÌ
    (check this in PDF content)

  16. Start
    7783
    Prefix
    ‚ÂÚÒÚ‚ÂÌÌÓ. 2. œÓÒÚÓÂÌË ‰‚ÛÒÚÓÓÌÌËı ÓˆÂÌÓÍ œÛÒÚ ̧ ̇ ÔÓ‚ÂıÌÓÒÚËS0, Ó„‡ÌË ̃Ë‚‡ ̨ ̆ÂÈ Ô‰ÒÚ‡‚ËÚÂÎ ̧Ì ̊È ̋ÎÂÏÂÌÚ, Á‡‰‡Ì ̊ ÍËÌÂχÚË ̃ÂÒÍË „‡ÌË ̃Ì ̊ ÛÒÎӂˡ, ÔË‚Ó‰ˇ ̆ËÂ Í ÌÂÔÂ ̊‚ÌÓÏÛ ‡ÒÔ‰ÂÎÂÌË ̨ ÔÂÂÏ ̆ÂÌËÈ, ÍÓÚÓÓÏÛ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨Ú ÍÓÏÔÓÌÂÌÚ ̊εij(M) = const(M∈V0) ÚÂÌÁÓ‡ ‰ÂÙÓχˆËË, ÒÓ‚Ô‡‰‡ ̨ ̆ËÂ Ò ÍÓÏÔÓÌÂÌÚ‡ÏË〈εij〉. “‡ÍÓ ‡ÒÔ‰ÂÎÂÌË ˇ‚ΡÂÚÒˇ ‰ÓÔÛÒÚËÏ ̊Ï ‰Îˇ ÙÛÌ͈ËÓ̇· À‡„‡Ìʇ
    Exact
    [49]
    Suffix
    , ‰ÓÒÚË„‡ ̨ ̆Â„Ó ÏËÌËÏÛχ ̇ ËÒÚËÌÌÓÏ ‡ÒÔ‰ÂÎÂÌËË ÔÂÂÏ ̆ÂÌËÈ, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ Ò Û ̃ÂÚÓÏ ‡‚ÂÌÒÚ‚ (5) Á‡ÔËÒ‡Ú ̧, ÓÔÛÒÚË‚ Ó·ÓÁ̇ ̃ÂÌË ÚÓ ̃ÍËM∈V0, 1 2 ∫ V0 C∗ijmnεmnεijdV> 1 2 ∫ V0 C∗ijmnε∗mnε∗ijdV= V0 2 Cijmn〈εmn〉〈εij〉dV, „‰ÂCijmn| ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C.
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  17. Start
    8207
    Prefix
    ‰ÂÎÂÌËË ÔÂÂÏ ̆ÂÌËÈ, ̃ÚÓ ÔÓÁ‚ÓΡÂÚ Ò Û ̃ÂÚÓÏ ‡‚ÂÌÒÚ‚ (5) Á‡ÔËÒ‡Ú ̧, ÓÔÛÒÚË‚ Ó·ÓÁ̇ ̃ÂÌË ÚÓ ̃ÍËM∈V0, 1 2 ∫ V0 C∗ijmnεmnεijdV> 1 2 ∫ V0 C∗ijmnε∗mnε∗ijdV= V0 2 Cijmn〈εmn〉〈εij〉dV, „‰ÂCijmn| ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C. ŒÚÒ ̨‰‡ ÒΉÛÂÚ 1 V0 ∫ V0 (C∗ijmn−Cijmn)dV>0.(6) ÕÂ‡‚ÂÌÒÚ‚‡ (6) ̋Í‚Ë‚‡ÎÂÌÚÌ ̊ ‰‚ÛÏ ÌÂ‡‚ÂÌÒÚ‚‡Ï, ÒÓ‰Âʇ ̆ËÏ ÎËÌÂÈÌ ̊ ËÌ‚‡ˇÌÚ ̊ ÚÂÌÁÓ‡ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ Ò ÍÓÏÔÓÌÂÌÚ‡ÏËC∗ijmn−Cijmn
    Exact
    [49,50]
    Suffix
    : 1 V0 ∫ V0 (C∗iimm−Ciimm)dV>0, 1 V0 ∫ V0 ( C∗imim− C∗iimm 3 −Cimim+ Ciimm 3 ) dV>0, ËÎË, Û ̃ËÚ ̊‚‡ˇ ËÁÓÚÓÔÌÓÒÚ ̧ ÚÂÌÁÓÓ‚̂C◦Ë̂CÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË Ï‡Úˈ ̊ Ë ÍÓÏÔÓÁËÚ‡ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ë ‡‚ÂÌÒÚ‚‡ (3), ÔÓÎÛ ̃‡ÂÏ C•iimmCV 9 +K◦(1−CV)>K, ( C•imim− C•iimm 3 ) CV+ 10G◦(1−CV)>10G,(7) „‰ÂC•ijmn| ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C•. œÛÒÚ ̧ ÚÂÔÂ ̧ ̇ ÔÓ‚ÂıÌÓÒÚËS0Á‡‰‡Ì ̊ ÒËÎÓ‚ ̊ „‡ÌË ̃Ì ̊ ÛÒÎӂˡ, ‚ ̊Á ̊‚‡ ̨
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  18. Start
    8793
    Prefix
    ̃‡ÂÏ C•iimmCV 9 +K◦(1−CV)>K, ( C•imim− C•iimm 3 ) CV+ 10G◦(1−CV)>10G,(7) „‰ÂC•ijmn| ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C•. œÛÒÚ ̧ ÚÂÔÂ ̧ ̇ ÔÓ‚ÂıÌÓÒÚËS0Á‡‰‡Ì ̊ ÒËÎÓ‚ ̊ „‡ÌË ̃Ì ̊ ÛÒÎӂˡ, ‚ ̊Á ̊‚‡ ̨ ̆Ë ‚ Ô‰ÒÚ‡‚ËÚÂÎ ̧ÌÓÏ ̋ÎÂÏÂÌÚ ̇ÔˇÊÂÌÌÓ ÒÓÒÚÓˇÌËÂ Ò ÍÓÏÔÓÌÂÌÚ‡ÏËσij(M) = const(M∈V0), ÒÓ‚Ô‡‰‡ ̨ ̆ËÏË Ò ÍÓÏÔÓÌÂÌÚ‡ÏË〈σij〉. “‡ÍÓ ‡ÒÔ‰ÂÎÂÌË ̇ÔˇÊÂÌËÈ ˇ‚ΡÂÚÒˇ ‰ÓÔÛÒÚËÏ ̊Ï ‰Îˇ ÙÛÌ͈ËÓ̇· ‡ÒÚËΡÌÓ
    Exact
    [49]
    Suffix
    , ‰ÓÒÚË„‡ ̨ ̆Â„Ó Ï‡ÍÒËÏÛχ ËÒÚËÌÌÓÏ ‡ÒÔ‰ÂÎÂÌËË Ì‡ÔˇÊÂÌËÈ. ›ÚÓ ‰‡ÂÚ ‚ÓÁÏÓÊÌÓÒÚ ̧ Ò Ò Û ̃ÂÚÓÏ ‡‚ÂÌÒÚ‚ (4) Á‡ÔËÒ‡Ú ̧, ÓÔÛÒÚË‚ Ó·ÓÁ̇ ̃ÂÌË ÚÓ ̃ÍËM∈V0, − 1 2 ∫ V0 S∗ijmnσmnσijdV6− 1 2 ∫ V0 S∗ijmnσ∗mnσ∗ijdV=− V0 2 Sijmn〈σmn〉〈σij〉dV, „‰ÂSijmn| ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂S.
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  19. Start
    10194
    Prefix
    ÚÓÓ„Ó ÌÂ‡‚ÂÌÒÚ‚‡ (8) | ÌËÊÌ ̨ ̨ ÓˆÂÌÍÛ ̋ÚÓ„Ó ÏÓ‰ÛΡ G−= 1 2 ( S•imim− S•iimm 3 ) CV 5 + 1−CV G◦ 6G.(11) —ΉÛÂÚ ÓÚÏÂÚËÚ ̧, ̃ÚÓ ÔË Á̇ ̃ËÚÂÎ ̧ÌÓÏ ‡ÁÎË ̃ËË ÛÔÛ„Ëı Ò‚ÓÈÒÚ‚ χÚˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ ÔÓÎÛ ̃ÂÌÌ ̊ ‰‚ÛÒÚÓÓÌÌË ӈÂÌÍË ÏÓ„ÛÚ Ó͇Á‡Ú ̧Òˇ ‰Ó‚ÓÎ ̧ÌÓ „Û· ̊ÏË. Œ‰ËÌ ËÁ ÔÓ‰ıÓ‰Ó‚, ÔÓÁ‚ÓΡ ̨ ̆ËÈ ÛÚÓ ̃ÌËÚ ̧ ÛÔÛ„Ë ı‡‡ÍÚÂËÒÚËÍË ‡ÒÒχÚË‚‡ÂÏÓ„Ó ÍÓÏÔÓÁËÚ‡, ÓÒÌÓ‚‡Ì ̇ ÏÂÚӉ ҇ÏÓÒӄ·ÒÓ‚‡Ìˡ
    Exact
    [1,3,6]
    Suffix
    . 3. ÃÂÚÓ‰ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ ŒÒÓ·ÂÌÌÓÒÚ ̧ ÔÓÒÚÓÂÌˡ ÓˆÂÌÍË ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡ Ò ̄‡Ó‚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË ÏÂÚÓ‰ÓÏ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ ÒÓÒÚÓËÚ ‚ Û ̃ÂÚ ‚Á‡ËÏÓ‰ÂÈÒڂˡ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÓ„Ó ̋ÎÂÏÂÌÚ‡ ÌÂÓ‰ÌÓÓ‰ÌÓÒÚË (‚ÍÎ ̨ ̃ÂÌˡ ËÎË ̃‡ÒÚˈ ̊ χÚˈ ̊) Ò Ó‰ÌÓÓ‰ÌÓÈ ËÁÓÚÓÔÌÓÈ Ò‰ÓÈ, ËÏ ̨ ̆ÂÈ ÓˆÂÌË‚‡ÂÏ ̊ ÏÓ‰ÛÎË ÛÔÛ„ÓÒÚË [1]. œÓÒÎÂ‰Û ̨ ̆ ÓÒ‰ÌÂÌË ÔÓ Ó· ̇ÂÏÛ ÍÓÏÔÓÁËÚ‡ ‚ÓÁÏÛ ̆ÂÌËÈ ‡ÒÔ‰ÂÎÂ
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  20. Start
    10527
    Prefix
    ÃÂÚÓ‰ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ ŒÒÓ·ÂÌÌÓÒÚ ̧ ÔÓÒÚÓÂÌˡ ÓˆÂÌÍË ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡ Ò ̄‡Ó‚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË ÏÂÚÓ‰ÓÏ Ò‡ÏÓÒӄ·ÒÓ‚‡Ìˡ ÒÓÒÚÓËÚ ‚ Û ̃ÂÚ ‚Á‡ËÏÓ‰ÂÈÒڂˡ ÓÚ‰ÂÎ ̧ÌÓ ‚ÁˇÚÓ„Ó ̋ÎÂÏÂÌÚ‡ ÌÂÓ‰ÌÓÓ‰ÌÓÒÚË (‚ÍÎ ̨ ̃ÂÌˡ ËÎË ̃‡ÒÚˈ ̊ χÚˈ ̊) Ò Ó‰ÌÓÓ‰ÌÓÈ ËÁÓÚÓÔÌÓÈ Ò‰ÓÈ, ËÏ ̨ ̆ÂÈ ÓˆÂÌË‚‡ÂÏ ̊ ÏÓ‰ÛÎË ÛÔÛ„ÓÒÚË
    Exact
    [1]
    Suffix
    . œÓÒÎÂ‰Û ̨ ̆ ÓÒ‰ÌÂÌË ÔÓ Ó· ̇ÂÏÛ ÍÓÏÔÓÁËÚ‡ ‚ÓÁÏÛ ̆ÂÌËÈ ‡ÒÔ‰ÂÎÂÌˡ Ô‡‡ÏÂÚÓ‚ ‚ ̋ÚËı ̋ÎÂÏÂÌÚ‡ı ÔÓÁ‚ÓΡÂÚ ÔÓÎÛ ̃ËÚ ̧ ‡Ò ̃ÂÚÌ ̊ Á‡‚ËÒËÏÓÒÚË ‰Îˇ ËÒÍÓÏ ̊ı ÛÔÛ„Ëı ı‡‡ÍÚÂËÒÚËÍ ÍÓÏÔÓÁËÚ‡. —̇ ̃‡Î‡ ‡ÒÒÏÓÚËÏ ÛÔÛ„Ó ‚Á‡ËÏÓ‰ÂÈÒÚ‚Ë ËÁÓÚÓÔÌÓ„Ó ̄‡Ó‚Ó„Ó ‚ÍÎ ̨ ̃ÂÌˡ Ò Á‡ÌËχ ̨ ̆ÂÈ ÌÂÓ„‡ÌË ̃ÂÌÌÛ ̨ ӷ·ÒÚ ̧ ÓÍÛʇ ̨ ̆ÂÈ Ò‰ÓÈ ËÁ ÚÓ„Ó Ê ÎËÌÂÈÌÓ ÛÔÛ„Ó„Ó Ï‡ÚÂˇ· Ò ÚÂÌÁÓÓÏ̂CÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔ
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  21. Start
    11479
    Prefix
    ≈ÒÎË Ï ̊ÒÎÂÌÌÓ ËÁ‚Π̃ ̧ ‚ÍÎ ̨ ̃ÂÌË ËÁ ÓÍÛʇ ̨ ̆ÂÈ Ò‰ ̊ Ë ·ÂÁ ËÁÏÂÌÂÌˡ Â„Ó Ì‡ÔˇÊÂÌÌÓ„Ó ÒÓÒÚÓˇÌˡ ÒÓÁ‰‡Ú ̧ ‚ ÌÂÏ ‰ÓÔÓÎÌËÚÂÎ ̧ÌÛ ̨ ‰ÂÙÓχˆË ̨, ÓÔ‰ÂΡÂÏÛ ̨ ÚÂÌÁÓÓψe′′, ÚÓ ÔÓÒΠ‚ÓÁ‚‡ ̆ÂÌˡ ‚ÍÎ ̨ ̃ÂÌˡ ̇ ÔÂÊÌ ÏÂÒÚÓ Â„Ó ‰ÂÙÓÏËÓ‚‡ÌÌÓ ÒÓÒÚÓˇÌË ·Û‰ÂÚ ÓÔ‰ÂÎˇÚ ̧ ÒÛÏχ ÚÂÌÁÓÓ‚ˆe0+ˆe′, ÔË ̃Âψe′′=̂W··ˆe′, „‰Â
    Exact
    [6]
    Suffix
    Ŵ= 3(1−ν) 1 +ν V̂+15 2 1−ν 4−5ν D̂.(12) œË ̋ÚÓÏ Ì‡ÔˇÊÂÌÌÓ ÒÓÒÚÓˇÌË ‚ÍÎ ̨ ̃ÂÌˡ ·Û‰ÂÚ ı‡‡ÍÚÂËÁÓ‚‡Ú ̧ ÚÂÌÁÓ ˆs′=̂C··(ˆe0+ˆe◦−ˆe′′) =̂C··(ˆe0+ˆe◦)−̂C··̂W··ˆe′.(13) “ÂÔÂ ̧ Á‡ÏÂÌËÏ ̄‡Ó‚Ó ‚ÍÎ ̨ ̃ÂÌË ڇÍËÏ Ê ‚ÍÎ ̨ ̃ÂÌËÂÏ, ÌÓ Ò‚ÓÈÒÚ‚‡ ÍÓÚÓÓ„Ó ÓÔ‰ÂΡÂÚ ÚÂÌÁÓ̂C•ÍÓ ̋ÙÙˈËÂÌÚÓ‚ ÛÔÛ„ÓÒÚË ‡Π̧ÌÓ„Ó ‚ÍÎ ̨ ̃ÂÌˡ ‚ ‡ÒÒχÚË‚‡ÂÏÓÏ ÍÓÏÔÓÁËÚÂ. œË Ó‰Ë̇ÍÓ‚ÓÈ ‰ÂÙÓχˆËË ‚ ÔÂÊÌÂÏ Ë ÌÓ‚ÓÏ ‚ÍÎ ̨ ̃
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  22. Start
    14736
    Prefix
    — Û ̃ÂÚÓÏ ÙÓÏÛÎ (1), (2) Ë (12) Ë Á‡‚ËÒËÏÓÒÚËνÓÚKËĠȉÂÏ Ĉ··̂W∗=(3K+4G)̂V+5G3K+4G 3K+6G D̂,̂C··̂W∗−̂C=4ĜV+G9K+8G 3K+6G D̂. ŒÔÂ‡ˆËˇ ÓÒ‰ÌÂÌˡ ÚÂÌÁÓÓ‚ ̃ÂÚ‚ÂÚÓ„Ó ‡Ì„‡ ‡‚ÌÓÒËÎ ̧̇ ‚ ̊ ̃ËÒÎÂÌË ̨ Ëı ‰‚Ûı ÎËÌÂÈÌ ̊ı ËÌ‚‡ˇÌÚÓ‚ ÔÛÚÂÏ ÔÓÎÌÓÈ Ò‚ÂÚÍË Ò ÚÂÌÁÓ‡ÏË̂VË̂D
    Exact
    [6,49]
    Suffix
    . “Ó„‰‡ Ò Û ̃ÂÚÓÏ ÙÓÏÛÎ ̊ (1) ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ËÁÓÚÓÔÌÓÈ Ï‡Úˈ ‡‚ÂÌÒÚ‚Ó (20) ·Û‰ÂÚ ̋Í‚Ë‚‡ÎÂÌÚÌÓ ÒËÒÚÂÏ ‰‚Ûı ‡Î„·‡Ë ̃ÂÒÍËı Û‡‚ÌÂÌËÈ            CV C•iimm/3 + 4G = 1 3K+ 4G − 1−CV 3K◦+ 4G , CV 6 ( C•imim−C•iimm/3 )K+ 2G 5 +G(9K+ 8G) = = 1 5G(3K+ 4G) − 1−CV 6G◦(K+ 2G) +G(9K+ 8G) , (21) ‰ÓÒÚ‡ÚÓ ̃Ì ̊ı ‰Îˇ ̇ıÓʉÂÌˡ ̋ÙÙÂÍÚË‚Ì ̊ı Á̇ ̃ÂÌËÈ Ó· ̇ÂÏÌÓ„Ó ÏÓ‰ÛΡKË ÏÓ‰ÛΡ Ò‰‚Ë„‡ G
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  23. Start
    17282
    Prefix
    ¬Ë‰ÌÓ, ̃ÚÓ ËÁÏÂÌÂÌË Á̇ ̃ÂÌˡK̇ ‰‚‡ ÔÓˇ‰Í‡ Ó͇Á ̊‚‡ÂÚ Ò··Ó ‚ÎˡÌË ̇ Á‡‚ËÒËÏÓÒÚË ̃GË̂GÓÚCV. ƒÎˇ ‡ÌËÁÓÚÓÔÌ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ Ò ÍÛ·Ë ̃ÂÒÍÓÈ ÒËÏÏÂÚËÂÈ ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C•ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ̃ÂÂÁ ÚË ̋ÎÂÏÂÌÚ‡C•11,C•12ËC•44ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ÂÈ ̋ÚÓÏÛ ÚÂÌÁÓÛ Ï‡Úˈ ̊ ̄ÂÒÚÓ„Ó ÔÓˇ‰Í‡
    Exact
    [51]
    Suffix
    . ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â [48,49]C•iimm/3 = 3/S•iimm=С•11+ 2C•12= 3K•, С•imim−C•iimm/3 = (2G•1−3G•2)ËS•imim−S•iimm/3 = 2/G•1+ 3/(2G•2), „‰ÂG•1= (С•11−C•12)/2 ËG•2=C•44. ›ÚË ‡‚ÂÌÒÚ‚‡ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ‚ ÒÓÓÚÌÓ ̄ÂÌˡı (9){(11) ÔË ‡Ò ̃ÂÚ Á‡‚ËÒËÏÓÒÚÂÈ ̃K+,̂K+Ë ̃K−,̂K−(ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ̄ÚËıÔÛÌÍÚËÌ ̊Â Ë ÔÛÌÍÚËÌ ̊ ÎËÌËË Ì‡ ËÒ.3) ÔËK= 0,1ËK= 10.
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  24. Start
    17304
    Prefix
    ¬Ë‰ÌÓ, ̃ÚÓ ËÁÏÂÌÂÌË Á̇ ̃ÂÌˡK̇ ‰‚‡ ÔÓˇ‰Í‡ Ó͇Á ̊‚‡ÂÚ Ò··Ó ‚ÎˡÌË ̇ Á‡‚ËÒËÏÓÒÚË ̃GË̂GÓÚCV. ƒÎˇ ‡ÌËÁÓÚÓÔÌ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ Ò ÍÛ·Ë ̃ÂÒÍÓÈ ÒËÏÏÂÚËÂÈ ÍÓÏÔÓÌÂÌÚ ̊ ÚÂÌÁÓ‡̂C•ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ̃ÂÂÁ ÚË ̋ÎÂÏÂÌÚ‡C•11,C•12ËC•44ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆ÂÈ ̋ÚÓÏÛ ÚÂÌÁÓÛ Ï‡Úˈ ̊ ̄ÂÒÚÓ„Ó ÔÓˇ‰Í‡ [51]. ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â
    Exact
    [48,49]
    Suffix
    C•iimm/3 = 3/S•iimm=С•11+ 2C•12= 3K•, С•imim−C•iimm/3 = (2G•1−3G•2)ËS•imim−S•iimm/3 = 2/G•1+ 3/(2G•2), „‰ÂG•1= (С•11−C•12)/2 ËG•2=C•44. ›ÚË ‡‚ÂÌÒÚ‚‡ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ ‚ ÒÓÓÚÌÓ ̄ÂÌˡı (9){(11) ÔË ‡Ò ̃ÂÚ Á‡‚ËÒËÏÓÒÚÂÈ ̃K+,̂K+Ë ̃K−,̂K−(ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ ̄ÚËıÔÛÌÍÚËÌ ̊Â Ë ÔÛÌÍÚËÌ ̊ ÎËÌËË Ì‡ ËÒ.3) ÔËK= 0,1ËK= 10.
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