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鎽樿锛?/span>
鏉愭枡鍔涘鏄熀纭€璇惧拰涓撲笟璇句箣闂寸殑妗ユ鍜岀航甯︼紝鏄嚑涔庢墍鏈夊伐绉戜笓涓氱殑鍩虹璇剧▼銆備紶缁熺殑鏉愭枡鍔涘鏁欐潗鍩轰簬绾垮脊鎬с€佸皬鍙樺舰銆佸悇椤瑰悓鎬х瓑鍩烘湰鍋囪锛屼笉鍙伩鍏嶅湴鍏锋湁寰堝ぇ鐨勫眬闄愭€с€傞珮鏂版妧鏈鑸┖鑸ぉ銆佽绠楁満銆佹柊鏉愭枡绛夌殑椋為€熷彂灞曪紝浣垮緱鐜版湁鐨勬暀鏉愬拰鏁欏浣撶郴涓庡煿鍏婚珮绱犺川鐨勬湰绉戠敓涓嶇浉閫傚簲銆傚姏瀛︽暀鏉愮殑缂栧啓涔熷簲璇ヤ笌鏃朵勘杩涳紝搴旇鑰冭檻鍚勭鏂版潗鏂欑殑澶嶆潅鐨勬湰鏋勫叧绯伙紝寮曞叆鏂扮殑瀹為獙鍐呭锛屽皢璁＄畻杞欢寮曞叆鍒拌璇惧唴瀹逛箣涓紝閫傚綋鐞嗚鑱旂郴瀹為檯锛屽悓鏃跺姞寮烘潗鏂欏姏瀛﹀彶鐭ヨ瘑鐨勮ˉ鍏呫€?/span>
鍏抽敭璇嶏細
鏉愭枡鍔涘锛涙柊鏉愭枡锛涙柊瀹為獙锛涜绠楄蒋浠讹紱鍔涘鍙?/span>
Liu Jian-lin
Department of Engineering Mechanics, China University of Petroleum, Qingdao 266555
Abstract:
Mechanics of Materials is a bridge or ligament between the fundamental and professional courses, which is the basis course of almost all engineering majors. The classical mechanics of materials is based upon the linear elasticity, infinitesimal deformation, and isotropic hypotheses, which has big constraints. High speed of high technologies, such aerospace, computer, and new materials, makes the now-used teaching materials and teaching system not adapt to cultivate the graduates with high diatheses. To compile the teaching materials about mechanics, we must adapt the developing of society. All kinds of complex constitutive relations about the new materials, new experiments, computational software, application of the theory and history of mechanics should be considered further.
Key word:
Mechanics of materials; new materials; new experiments; computational software; history of mechanics
1. 寮曡█
鏉愭枡鍔涘(mechanics of materials)浣滀负鏈烘銆佸湡鏈ㄣ€侀噰鐭裤€佽埅绌鸿埅澶┿€佺煶娌瑰伐
绋嬨€佸湴璐ㄥ嫎鎺€佹捣娲嬪伐绋嬬瓑棰嗗煙鐨勫熀纭€瀛︾锛屽湪璁捐銆佸埗閫犱笌鐢熶骇銆佹妧鏈垱鏂般€佸浜ф帾鏂界瓑鏂归潰鍏锋湁閲嶈鐨勪綔鐢紝鏄悊宸ョ澶т笓闄㈡牎鐩稿叧涓撲笟鐨勪竴闂ㄩ噸瑕佺殑涓撲笟鍩虹璇剧▼銆傛潗鏂欏姏瀛︽槸鍩虹璇惧拰涓撲笟璇句箣闂寸殑妗ユ鍜岋紝璧峰埌鎵夸笂鍚笅鐨勪綔鐢ㄣ€傚畠鏃㈠叿鏈夊熀纭€姒傚康鍜岀悊璁虹殑鐗圭偣锛屽張鍏锋湁閽卞妫墍鎻愬€＄殑“鎶€鏈瀛?/span>(engineering mechanics)”鏈夐噸瑕佸簲鐢ㄤ环鍊肩殑涓€闈紱浣嗗畠鏃笉鍚屼簬鏁扮悊鍖栫敓鐗╃瓑瀛︾鐨勬洿鍔犱晶閲嶄簬鍩虹鎬э紝鍙堜笉鍚屼簬鏇村姞瀹炵敤鐨勫叿浣撶殑搴旂敤瀛︾銆傚洜鑰岋紝鍏充簬鏉愭枡鍔涘璇剧▼濡備綍鏉ヨ锛屼互鍙婃潗鏂欏姏瀛︽暀鏉愬浣曠紪鍐欙紝涓€鐩存槸涓€涓簤璁轰笉浼戠殑骞朵笖闅惧害寰堝ぇ鐨勮瘽棰樸€?/span>
鏉愭枡鍔涘璧锋簮浜?/span>17涓栫邯锛屽湪绉戝宸ㄥ尃杈?/span>鑺銆佷冀鍒╃暐銆佹儬鏇存柉銆佸簱浼︺€侀害鍏嬫柉闊︺€佹鎷夈€佹煰瑗裤€佹堡濮嗘柉 鏉ㄣ€佷集鍔埄銆佺撼缁村彾銆佸湥缁村崡绛変汉鐨勫姫鍔涗笅锛屽舰鎴愪簡涓€闂ㄧ郴缁熺殑绉戝銆傛棭鏈熺殑鏉愭枡鍔涘鏄互鏈ㄦ潗銆佺煶澶寸瓑鑴嗘€ф潗鏂欎负鐮旂┒涓婚锛岀敱浜庡叾鍙樺舰寰堝皬锛屾墍浠ヤ笉鍙伩鍏嶅湴鍏锋湁寰堝ぇ鐨勫眬闄愭€с€?/span>19涓栫邯涓彾锛岀嚎寮规€ч棶棰樼殑鑳″厠瀹氬緥浠ュ強鍧囧寑杩炵画銆佸悇鍚戝悓鎬х殑鍩烘湰鍋囧畾鎴愪负鏉愭枡鍔涘鐨勫熀纭€銆傜幇鍦ㄥ浗鍐呭娴佽鐨勬潗鏂欏姏瀛︽槸鍦?/span>20涓栫邯50骞翠唬寮曠敤鍓嶈嫃鑱旂殑鏁欐潗鍜屾暀瀛︽ā寮忕殑鍩虹涓婂缓绔嬭捣鏉ョ殑銆傞殢鐫€楂樻柊鎶€鏈鑸┖鑸ぉ銆佽绠楁満銆佹柊鏉愭枡绛夌殑椋為€熷彂灞曪紝鍔涘鏁欏鐨勫唴瀹瑰拰鏁欏鏂规硶涔熷彂鐢熶簡寰堝ぇ鐨勫彉鍖栵紝杩欎娇寰楃幇鏈夌殑鏁欐潗鍜屾暀瀛︿綋绯讳笌鍩瑰吇楂樼礌璐ㄧ殑鏈鐢熶笉鐩搁€傚簲[1, 2]銆傚姏瀛︽暀鏉愮殑缂栧啓涔熷簲璇?/span>“涓庢椂淇辫繘”锛屼笉鏂湴鍚告敹鏂扮敓鐨勬蹇靛拰鏂规硶鎵嶈兘涓嶆柇瀹屽杽銆?/span>
2. 鏉愭枡鍔涘鏁欐潗鐜扮姸
瀵规潗鏂欏姏瀛︽暀鏉愬仛鍑洪噸澶ц础鐚殑绉戝瀹跺簲棣栨帹閾佹懇杈涙煰(Timoshenko, S. P.)鏁欐巿銆備粬浜?/span>1908骞村湪鍦ｅ郊寰楀牎閾侀亾宸ョ▼瀛﹂櫌浠绘暀鏃跺氨鍑虹増浜嗕粬鐨勭涓€鏈€婃潗鏂欏姏瀛︺€嬫暀鏉愩€?/span>1930骞达紝鍙堝嚭鐗堜簡钁楀悕鐨勩€?/span>Strength of Materials銆嬶紝寰堝揩灏遍闈″叏鐞冿紝涓€鏃舵礇闃崇焊璐点€?/span>1972骞达紝閾佹懇杈涙煰鍙堝嚭鐗堜簡銆?/span>Mechanics of Materials銆嬶紝鍙嶆槧浜嗗綋鏃舵潗鏂欏姏瀛︾殑鏈€鏂拌繘灞曘€傞櫎姝や箣澶栵紝姣旇緝鏈夊奖鍝嶇殑鏁欐潗鏄垪瀹佹牸鍕掗搧閬撳闄㈡暀鎺堝埆杈借€跺か浜?/span>1932骞存墍钁楃殑銆婃潗鏂欏姏瀛︺€嬫暀鏉愶紝涔熸浘缁忓娆″啀鐗?/span>[3]銆?/span>
鎴戝浗浜?/span>1975骞寸敱鏉滃簡鍗庢暀鎺堢瓑浜虹紪钁椾簡绗竴鏈€婃潗鏂欏姏瀛︺€嬨€?/span>1965骞达紝瀛欒鏂规暀鎺堢瓑浜哄嚭鐗堜簡鍙﹀涓€鏈€婃潗鏂欏姏瀛︺€嬫暀鏉愶紝浣夸箣鏇村姞閫傚悎涓浗涓€鑸伐绉戦櫌鏍＄殑鐗圭偣銆傚叾瀹冪殑鏈夐噸瑕佸奖鍝嶇殑鏁欐潗杩樻湁锛氬垬楦挎枃鏁欐巿涓荤紪鐨勩€婃潗鏂欏姏瀛︺€嬶紝鑻忕考鏋楁暀鎺堜富缂栫殑銆婃潗鏂欏姏瀛︺€嬨€佸崟绁栬緣鏁欐巿涓荤紪鐨勩€婃潗鏂欏姏瀛︺€嬨€佽寖閽︾強鏁欐巿涓荤紪鐨勩€婃潗鏂欏姏瀛︺€嬩互鍙娿€婂伐绋嬪姏瀛︺€嬬郴鍒楃瓑绛夈€傝繖浜涙暀鏉愰櫎浜嗕繚鎸佷紶缁熸暀鏉愮殑姒傚康娓呮櫚銆佺粨鍚堝疄闄呯瓑鐗圭偣浠ュ锛岃繕鍦ㄧ獊鐮寸幇鏈夌殑鍐呭浣撶郴銆侀檲鏃х殑璁粌鏂瑰紡銆佷紶缁熺殑鍗曚竴鏁欏妯″紡绛夋柟闈㈠仛浜嗕竴浜涘垵姝ユ帰绱?/span>[4]銆?/span>
3. 鏂颁笘绾潗鏂欏姏瀛︾殑闈╂柊
鑷?/span>20涓栫邯60骞翠唬浠ユ潵锛岄殢鐫€宸ヤ笟鎶€鏈殑楂樺害鍙戝睍锛屽疄楠岃澶囨棩瓒嬪畬鍠勶紝瀹為獙鎶€鑳戒笉鏂彁楂橈紝杩欎娇寰楁潗鏂欏姏瀛︽墍娑夊強鐨勯鍩熸洿鍔犲骞裤€佹墍鍖呭惈鐨勭煡璇嗘洿鍔犱赴瀵屽褰┿€傝繖浜涙柊鐨勫彉闈╁鏉愭枡鍔涘鐨勬暀鏉愮紪鍐欐彁鍑轰簡鏇撮珮鐨勮姹傦紝杩欎簺瑕佹眰鍏蜂綋琛ㄧ幇鍦細
锛?锛?span style="FONT: 7pt 'Times New Roman'"> 鍚勭鏂版潗鏂欏眰鍑轰笉绌凤紝蹇呴』閫傚綋鑰冭檻鍏舵湰鏋勫叧绯伙紱
绠€鍗曟潵璇达紝鏉愭枡鍔涘鏄爺绌舵潗鏂欎笌缁撴瀯鐨勫姏瀛︼紱浣嗘槸浼犵粺鐨勬潗鏂欏姏瀛﹂兘鏄潰
鍚戝鐞嗗悇鍚戝悓鎬с€佺嚎寮规€с€佸皬鍙樺舰銆佹棤鍒濆簲鍔涖€佸潎鍖€杩炵画鐨勬潗鏂欙紝杩欐棤褰箣涓檺鍒朵簡鍏跺簲鐢ㄨ寖鍥淬€傝嚜20涓栫邯50骞翠唬浠ユ潵锛屽ぇ閲忕殑鏂版潗鏂欎笉鏂粠鍐涘伐涓庨珮绉戞妧棰嗗煙鎵╁睍鍒拌澶氬伐涓氶儴闂ㄣ€傝繖浜涙潗鏂欙紝渚嬪澶嶅悎鏉愭枡銆侀珮鍒嗗瓙鏉愭枡銆佺粨鏋勯櫠鐡枫€佹櫤鑳芥潗鏂欑瓑澶ч噺浣跨敤锛屽ぇ澶у噺杞讳簡缁撴瀯鐨勯噸閲忥紝鎻愰珮浜嗙粨鏋勭殑寮哄害鍜屽鍛姐€?/span>
浣嗘槸缁忓吀鐨勫熀浜庤儭鍏嬪畾寰嬬殑绾垮脊鎬у皬鍙樺舰鏈瀯鍏崇郴宸茬粡鏃犳硶鎻忚堪涓婅堪鏉愭枡鐨勫搷搴旓紝渚嬪锛氳埅绌洪鍩熷ぇ閲忛噰鐢ㄧ殑绾ょ淮鎴栬€呴绮掑寮哄鍚堟潗鏂欐湰韬负鍚勫悜寮傛€э紱宸ョ▼涓ぇ閲忓惈鏈夎绾圭殑鏉愭枡宸查潪鍧囧寑杩炵画锛涢珮鍒嗗瓙鏉愭枡鐨勫簲鍔?/span>–搴斿彉鍏崇郴鏄笌鏃堕棿鐩稿叧鐨勶紝涓斿ぇ閮戒负闈炵嚎鎬э紱鏂板瀷鐨?/span>“杞墿璐?/span>”鏉愭枡鏄粙浜庡浐浣撲笌娴佷綋涔嬮棿鐨勭壒娈婄殑“澶嶆潅娴佷綋”锛岃繕娌℃湁鎭板綋鐨勬湰鏋勫叧绯伙紱纰崇撼绫崇锛?/span>CNT锛夊拰鍏跺畠鐢熺墿鏉愭枡鍏锋湁鍙嶅父鐨?/span>“璐熸硦鏉炬瘮”鏁堝簲锛涚敓鐗╀綋涓殑鏌愪簺鏉愭枡鍏?/span>“闆跺簲鍔?/span>”鐐瑰苟闈炰负鍏跺垵濮嬬姸鎬侊紱缁嗚優绮橀檮鏃堕渶瑕佽€冭檻鍏跺畠鐨?/span>“闈炵粡鍏稿姏”锛屽姣涚粏鍔涖€佽寖寰峰崕鍔涚殑褰卞搷銆傝繖浜涚幇璞￠兘璇存槑锛屾柊鐨勬潗鏂欏姏瀛︽暀鏉愬繀椤诲寘鍚互涓婂悇绉嶆柊鐨勭幇璞★紝渚嬪闈炲潎鍖€銆佸悇鍚戝紓鎬с€侀潪绾挎€с€佹椂闂寸浉鍏崇瓑鍥犵礌銆?/span>
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浼犵粺鐨勬潗鏂欏姏瀛︽祴璇曚华鍣ㄤ富瑕佹湁鏉愭枡涓囪兘璇曢獙鏈恒€佺柌鍔宠瘯楠屾満銆佸啿鍑绘祴璇曚华銆?/span>
鎵浆娴嬭瘯浠€佸厜寮逛华銆佺數娴嬬瓑锛岃繖浜涙祴璇曟妧鏈瘮杈冮檲鏃э紝瀵逛簬瀛︾敓鍚彂鎬т笉澶с€傝€岄殢鐫€淇℃伅鎶€鏈殑鍙戝睍锛屽悇绉嶆祴璇曡澶囩殑绮惧害瓒婃潵瓒婇珮锛屽悇绉嶆祴璇曠殑鎵嬫涔熻秺鏉ヨ秺澶氾紝浠ヨ嚦浜庤繃鍘诲緢澶氭棤娉曞疄鐜扮殑瀹為獙鐜板湪寰堢畝鍗曞湴鍙互瀹屾垚銆備緥濡傦紝鐮旂┒鏉愭枡鐨勫井绾宠缁撴瀯鏃讹紝杩囧幓缁忓父浣跨敤鐨勯噾鐩告樉寰暅宸茬粡琚壂鎻忕數瀛愭樉寰暅锛?/span>SEM锛夈€佹壂鎻忛毀閬撴樉寰暅锛?/span>STM锛夈€佸拰鍘熷瓙鍔涙樉寰暅锛?/span>AFM锛夌瓑楂樼簿搴︾數闀滄墍鍙栦唬锛岃€岃繖浜涙樉寰暅浠ュ強閰嶅鐨勫姞杞借缃兘寰堝鏄撳疄鐜板井绾宠灏哄害鐨勫姏瀛︽祴璇曘€傚湪鍏夋祴棰嗗煙锛屽綋浠婅繀閫熷彂灞曡捣鏉ョ殑浜戠汗娉曘€佷簯绾瑰共娑夋硶銆佺數闀滀簯绾规硶銆佺數瀛愭暎鏂戝共娑夋硶銆佹暟瀛楃浉鍏虫硶绛夋柊鍨嬬殑鎵嬫宸茬粡閫愭笎鍙栦唬浜嗗厜寮规祴璇曘€傝€屽浜庨珮鍒嗗瓙鏉愭枡銆佽蒋鐗╄川鏉愭枡銆佺敓鐗╂潗鏂欏楠ㄩ銆佽倢鑲夈€佸績鑴忕瓑鐨勫姏瀛︽€ц兘娴嬭瘯锛屾洿涓嶈兘浣跨敤浼犵粺鐨勪华鍣ㄦ潵杩涜瀹為獙锛屾墍浠ョ幇鍦ㄥ皻杩樼己涔忓畬鍠勭殑璁惧锛屼絾杩欎簺闂鐨勮В鍐冲嵈杩湪鐪夌潾銆?/span>
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鏂版椂鏈熸潗鏂欏姏瀛﹂櫎浜嗗簲璇ュ煿鍏诲鐢熷垎鏋愰棶棰樼殑鑳藉姏銆佸姞娣卞鐢熷鍩烘湰姒傚康鍜?/span>
鍩烘湰鐞嗚鐨勭悊瑙ｄ互澶栵紝灏氬簲璇ユ帉鎻＄敤璁＄畻鏈鸿В鍐冲疄闄呴棶棰樼殑鑳藉姏銆傛棭鍦?/span>1997骞?/span>9鏈堬紝閽卞妫櫌澹凡缁忛瑙佸埌浜嗚绠楁妧鏈殑閲嶈鎬э紝浠栧湪涓烘竻鍗庡ぇ瀛﹀伐绋嬪姏瀛︾郴寤虹郴40鍛ㄥ勾鐨勮春淇′腑鍐欓亾锛?/span>“闅忕潃鍔涘璁＄畻鑳藉姏鐨勬彁楂橈紝鐢ㄥ姏瀛︾悊璁鸿В鍐宠璁￠棶棰樻垚涓轰富瑕侀€斿緞锛岃€岃瘯楠屾墜娈垫垚涓烘瑕佺殑浜嗐€傜敱姝ゅ睍鏈?/span>21涓栫邯锛屽姏瀛﹀姞鐢靛瓙璁＄畻鏈哄皢鎴愪负宸ョ▼璁捐鐨勪富瑕佹墜娈碉紝灏辫繛宸ョ▼鍨嬪彿鐮斿埗涔熷彧鐢ㄧ數瀛愯绠楁満鍔犲舰璞℃樉绀恒€傞兘鏄櫄鐨勶紝涓嶆槸瀹炵殑锛屾墍浠ョО涓?/span>“铏氭嫙鍨嬪彿鐮斿埗”锛?/span>virtual prototyping锛夈€傛渶鍚庡氨鏄疄鐗╃敓浜т簡銆?/span>”鐜版湁鐨勫悇绉嶆暟鍊艰蒋浠跺凡缁忕粰鍔涘瑙ｅ喅瀹為檯闂鎻愪緵浜嗘湁鍔涚殑宸ュ叿锛屽澶у瀷鏈夐檺鍏冭蒋浠?/span>ANSYS銆?/span>ABAQUS锛屾暟鍊艰绠楄蒋浠?/span>Matlab銆?/span>Maple銆?/span>Mathematica绛夛紝閮藉惈鏈夊ぇ閲忕殑瀛愮▼搴忓簱锛屽叿鏈夎壇濂界殑鍥惧舰澶勭悊鍔熻兘銆傜啛缁冧娇鐢ㄨ繖浜涜蒋浠剁殑鑳藉姏鐨勫煿鍏诲浜庡鐢熶互鍚庤兘澶熷緢蹇繁鍏ヨВ鍐冲疄闄呴棶棰樿捣鐫€涓嶅彲蹇界暐鐨勪綔鐢ㄣ€?/span>
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澶ч儴鍒嗗伐绉戦櫌鏍＄殑鏉愭枡鍔涘鏁欐潗搴旇纭疄鑳藉璧峰埌鎵垮墠鍚悗鐨勪綔鐢紝搴旇灏嗗姏瀛︾悊璁轰笌宸ョ▼瀹為檯宸у鍦扮粨鍚堝湪涓€璧枫€傚瀵逛簬鏉愭枡鐨勫姏瀛︽€ц兘锛屽彲浠ュ垪涓炬柊鏉愭枡鍦ㄨ埅绌鸿埅澶╋紙绁炰簲绁炲叚锛夈€佹苯杞︺€佹満姊扮瓑鏂归潰鐨勫簲鐢紱瀵逛簬寮哄害鏍℃牳锛屽彲浠ョ粨鍚堣嚜宸辩殑绉戠爺浣撲細锛岃杩板湪鐭虫补宸ョ▼銆佹捣娲嬪伐绋嬨€侀鏈恒€佸湴璐ㄧ瓑棰嗗煙鐨勫簲鐢紱璁茶堪鍘嬫潌绋冲畾鏃讹紝鍙互鍒椾妇鍘嗗彶涓婃湭鑰冭檻鍘嬫潌绋冲畾鐨勫け浜嬮噸澶т緥瀛愮瓑绛夈€傛€讳箣锛岃杩版煇涓€涓棶棰樻椂锛屽嬁蹇呭己璋冨叾纭垏鐨勫簲鐢紝涓嶈鍙ｈ嫢鎮渤锛岃浜嗕竴澶у爢鐞嗚锛屼絾鏄渶缁堜护瀛︾敓涓嶇煡閬撳浣曞簲鐢ㄣ€傝繖浣垮緱鎴戜滑搴旇鍚戣€佷竴杈堢殑鍔涘瀹讹紝濡傛灄瀹剁繕鍏堢敓瀛︿範銆傛灄鍏堢敓鍦ㄩ夯鐪佺悊宸ュ闄㈣鎺堥珮绛夋暟瀛︽椂锛屽氨浠庡伐绋嬭€屼笉鏄崟绾殑鏁板璇佹槑鍏ユ墜锛屼粠鑰屼娇璇ヨ绋嬪彉鎴愮儹闂ㄦ姠鎵嬭銆?/span>
锛?锛?span style="FONT: 7pt 'Times New Roman'"> 鏉愭枡鍔涘鍙查渶瑕佸姞寮猴紝鍚屾椂涓嶆柇琛ュ厖鏂扮殑姒傚康銆?/span>
绗旇€呰涓猴紝璁茶堪涓€闂ㄨ绋嬶紝搴旇鍚戝鐢熻杩拌繖闂ㄨ绋嬬殑鍙戝睍鍘嗗彶锛屼互鍙婇€傚綋
琛ュ厖瀵硅繖闂ㄥ绉戝仛鍑洪噸澶ц础鐚殑绉戝瀹剁殑浜嬭抗銆傛潗鏂欏姏瀛︽槸涓€闂ㄥ彜鑰佺殑瀛︾锛岄櫎浜嗗巻鍙蹭笂閭ｄ簺浼熷ぇ鐨勭瀛﹀鐨勮础鐚箣澶栵紝闇€瑕佽ˉ鍏呰繎浠ｆ潗鏂欏姏瀛︾殑鍙戝睍鍙层€備緥濡傝捣婧愪簬寰峰浗鐨勫摜寤锋牴瀛︽淳锛屽湪鍏嬭幈鍥狅紙Klein, F.锛夊拰甯屽皵浼壒锛?/span>Hilber, D.锛夌殑鎺ㄥ姩涓嬶紝褰㈡垚浜嗕互鏅湕鐗癸紙Prandtl, L.锛変负棣栫殑杩戜唬搴旂敤鍔涘瀛︽淳銆傚湪鍝ュ环鏍瑰ぇ瀛︼紝鏅湕鐗瑰煿鍏诲嚭浜嗕竴澶ф壒鐨勫姏瀛﹀ぇ甯堬紝濡傚啹 鍗￠棬銆侀搧鎽╄緵鏌€佸笇灏斻€佸痉椴佸厠銆佹櫘鎷夋牸銆侀偅鎴淬€侀倱鍝堟墭绛夐兘鏄摜寤锋牴瀛︽淳鐨勬澃鍑轰唬琛ㄣ€傝€屽湪鍗庤鍔涘瀹朵腑锛屼篃鏈夊ぇ閲忕殑鏉板嚭浜虹墿锛屼緥濡傚簲鐢ㄦ暟瀛﹀鏋楀缈樸€佽瑾変负“鐢熺墿鍔涘涔嬬埗”鐨勫啹鍏冩、銆佽绠楀姏瀛﹀鍗炲鐠溿€佹祦浣撳姏瀛﹀鍚磋€€绁栥€?ldquo;棰勫簲鍔涗箣鐖?rdquo;鏋楀悓鐐庣瓑銆傛垜鍥界殑搴旂敤鍔涘鐨勬簮澶翠篃鍦ㄥ摜寤锋牴锛屽叾浠ｈ〃浜虹墿鏈夐挶瀛︽．銆侀挶浼熼暱銆佸懆鍩规簮銆侀儹姘告€€銆佸紶缁淬€侀挶浠ゅ笇銆佽儭娴锋槍銆侀檰澹槈绛?/span>[5]銆?/span>
闄や簡瀵瑰凡鏈夊姏瀛﹀彶鐨勯槓杩颁箣澶栵紝杩樺簲璇ュ鍔涘鍙や唬鍙蹭笌杩戜唬鍙茬殑鎸栨帢锛屼緥濡傛垜鍥藉鑰呰€佷寒鏁欐巿鑰冭瘉鍑轰簡鑳″厠瀹氬緥搴旂О涓?ldquo;閮戠巹–鑳″厠瀹氬緥”锛屽洜涓烘垜鍥藉彜浠ｅ鑰呴儜鐜勬瘮鑳″厠鏃╀簡1500骞村彂鐜颁簡寮规€у畾寰嬨€傚啀姣斿锛岀洰鍓嶉€氱敤鐨?/span>Mises鍑嗗垯锛屽疄闄呬笂鐢辨尝鍏扮瀛﹀鑳′集鏈€鏃╂彁鍑猴紝搴旇绉颁负Huber-Mises鍑嗗垯杈冧负纭垏銆傝€屽湪璁叉巿灞堟湇鍑嗗垯鏃讹紝杩樺簲璇ユ彁鍙婃垜鍥藉鑰呫€佽タ瀹変氦閫氬ぇ瀛︽暀鎺堜繛鑼傚畯鎻愬嚭鐨?ldquo;鍙屽壀鍒囩悊璁?rdquo;銆傝繖浜涗簨杩归兘瓒充互婵€璧峰鐢熺殑寮虹儓鐨勬皯鏃忚嚜灏婂績锛屼粠鑰屾縺鍙戜粬浠殑瀛︿範鍏磋叮銆?/span>
4. 缁撹
鍔涘鏁欐潗鐨勭紪鍐欓渶瑕佷笌鏃朵勘杩涳紝闄や簡瑕佷繚鎸佷紶缁熸暀鏉愮殑姒傚康娓呮櫚銆佺粨鍚堝疄闄呯瓑鐗圭偣浠ュ锛岃繕搴旇绐佺牬鐜版湁鐨勫唴瀹逛綋绯汇€侀檲鏃х殑璁粌鏂瑰紡銆佷紶缁熺殑鍗曚竴鏁欏妯″紡銆傜幇浠ｆ潗鏂欏姏瀛︽墍娑夊強鐨勯鍩熸洿鍔犲骞裤€佹墍鍖呭惈鐨勭煡璇嗘洿鍔犱赴瀵屽褰╋紝杩欎簺鏂扮殑鍙橀潻瀵规潗鏂欏姏瀛︾殑鏁欐潗缂栧啓鎻愬嚭浜嗘洿楂樼殑瑕佹眰锛屼娇寰楁垜浠簲璇ヨ€冭檻鍚勭鏂版潗鏂欑殑澶嶆潅鐨勬湰鏋勫叧绯伙紱蹇呴』鍙婃椂鏇存柊璁惧锛屽紩鍏ユ柊鐨勫疄楠屽唴瀹癸紱蹇呴』灏嗚绠楄蒋浠跺紩鍏ュ埌璁茶鍐呭涔嬩腑锛涘繀椤荤悊璁鸿仈绯诲疄闄咃紝鍒囧繉绾镐笂璋堝叺锛涘繀椤诲姞寮烘潗鏂欏姏瀛﹀彶鐭ヨ瘑鐨勮ˉ鍏呫€傚湪鏉愭枡鍔涘鐨勬暀鏉愮紪鍐欐柟闈紝鎴戜滑杩樺簲璇ヤ笉鏂?/span>鐮旂┒銆佷笉鏂垱鏂般€佷笉鏂疄璺碉紝鏈€缁堜负寤鸿涓庡嚭鐗堝叿鏈夋垜鍥界壒鑹茬殑浼樼鍔涘鏁欐潗濂犲畾鍩虹銆?span lang="EN-US">
[1] 鑼冮挦鐝?/span>, 鐜嬫尝, 娈烽泤淇?/span>. 鏉愭枡鍔涘 [M]. 鍖椾含锛氶珮绛夋暀鑲插嚭鐗堢ぞ锛?/span>1998.
[2] 鍙跺織鏄?/span>, 榛勬瘏. 鍔犲己鍥藉鍔涘鏁欐潗鐮旂┒, 淇冭繘鎴戝浗浼樼鏁欐潗寤鸿 [J]. 涓浗澶у鏁欏, 2007, 5: 11–12.
[3] 榛勬瘏. 鍏充簬“鍗佷簲”鍔涘鏁欐潗寤鸿鐨勬€濊€?/span>. 鍔涘涓庡疄璺?/span>, 2001, 23: 68–70.
[4] 姝﹀缓鍗?/span>, 寰愬缓鏇?/span>, 鍒樺痉鍗?/span>. 鍏充簬缂栧啓鏉愭枡鍔涘鏁欐潗鐨勬€濊€?/span>. 楂樼瓑寤虹瓚鏁欒偛, 2001, 41: 62–63.
[5] 姝﹂檯鍙?/span>. 鍔涘鍙?/span> [M]. 閲嶅簡锛氶噸搴嗗嚭鐗堢ぞ锛?/span>2000.
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