{"id":482,"date":"2025-04-21T23:40:03","date_gmt":"2025-04-21T15:40:03","guid":{"rendered":"https:\/\/blog.zangzheyi.top\/?p=482"},"modified":"2025-04-21T23:40:03","modified_gmt":"2025-04-21T15:40:03","slug":"%e3%80%90%e8%bd%ac%e8%bd%bd%e3%80%91%e5%8a%9b%e5%ad%a6%e4%b8%ad%e7%9a%84%e5%90%84%e7%a7%8d%e6%a8%a1%e9%87%8f%e6%a6%82%e5%bf%b5%ef%bc%8c%e4%bd%a0%e9%83%bd%e5%8c%ba%e5%88%86%e6%b8%85%e6%a5%9a%e4%ba%86","status":"publish","type":"post","link":"https:\/\/blog.zangzheyi.top\/index.php\/2025\/04\/21\/%e3%80%90%e8%bd%ac%e8%bd%bd%e3%80%91%e5%8a%9b%e5%ad%a6%e4%b8%ad%e7%9a%84%e5%90%84%e7%a7%8d%e6%a8%a1%e9%87%8f%e6%a6%82%e5%bf%b5%ef%bc%8c%e4%bd%a0%e9%83%bd%e5%8c%ba%e5%88%86%e6%b8%85%e6%a5%9a%e4%ba%86\/","title":{"rendered":"\u3010\u8f6c\u8f7d\u3011\u529b\u5b66\u4e2d\u7684\u5404\u79cd\u6a21\u91cf\u6982\u5ff5\uff0c\u4f60\u90fd\u533a\u5206\u6e05\u695a\u4e86\u5417\uff1f"},"content":{"rendered":"\n
\n

\u672c\u6587\u7531 \u7b80\u60a6 SimpRead<\/a> \u8f6c\u7801\uff0c \u539f\u6587\u5730\u5740 mp.weixin.qq.com<\/a><\/p>\n<\/blockquote>\n\n\n\n

\u70b9\u51fb\u84dd\u8272\u5c0f\u5b57\u4e00\u952e\u5173\u6ce8\uff0cCAE \u4eff\u771f\u4e0d\u8ff7\u8def<\/p>\n\n\n\n

“\u6a21\u91cf” \u53ef\u4ee5\u7406\u89e3\u4e3a\u662f\u4e00\u79cd\u6807\u51c6\u91cf\u6216\u6307\u6807\u3002\u6750\u6599\u7684 “\u6a21\u91cf” \u4e00\u822c\u524d\u9762\u8981\u52a0\u8bf4\u660e\u8bed\uff0c\u5982\u5f39\u6027\u6a21\u91cf\u3001\u538b\u7f29\u6a21\u91cf\u3001\u526a\u5207\u6a21\u91cf\u3001\u622a\u9762\u6a21\u91cf\u7b49\uff0c\u8fd9\u4e9b\u90fd\u662f\u4e0e\u53d8\u5f62\u6709\u5173\u7684\u6307\u6807\u3002<\/p>\n\n\n\n

(1) \u6768\u6c0f\u6a21\u91cf (Young Modulus)\uff1a<\/strong><\/p>\n\n\n\n

\u6768\u6c0f\u6a21\u91cf\u5c31\u662f\u5f39\u6027\u6a21\u91cf\uff0c\u8fd9\u662f\u6750\u6599\u529b\u5b66\u91cc\u7684\u4e00\u4e2a\u6982\u5ff5\u3002\u5bf9\u4e8e\u7ebf\u5f39\u6027\u6750\u6599\u6709\u516c\u5f0f\u03c3(\u6b63\u5e94\u529b)=E*\u03b5(\u6b63\u5e94\u53d8) \u6210\u7acb\uff0c\u5f0f\u4e2d\u03c3\u4e3a\u6b63\u5e94\u529b\uff0c\u03b5\u4e3a\u6b63\u5e94\u53d8\uff0cE \u4e3a\u5f39\u6027\u6a21\u91cf\uff0c\u662f\u4e0e\u6750\u6599\u6709\u5173\u7684\u5e38\u6570\uff0c\u4e0e\u6750\u6599\u672c\u8eab\u7684\u6027\u8d28\u6709\u5173\u3002<\/p>\n\n\n\n

\u6768 (ThomasYoung1773\uff5e1829) \u7814\u7a76\u4e86\u6750\u6599\u7684\u526a\u5f62\u53d8\uff0c\u8ba4\u4e3a\u526a\u5e94\u529b\u662f\u4e00\u79cd\u5f39\u6027\u5f62\u53d8\u3002 1807 \u5e74\uff0c\u4ed6\u63d0\u51fa\u5f39\u6027\u6a21\u91cf\u7684\u5b9a\u4e49\uff0c\u4e3a\u6b64\u540e\u4eba\u5c06\u5f39\u6027\u6a21\u91cf\u79f0\u4e3a\u6768\u6c0f\u6a21\u91cf\u3002\u94a2\u7684\u6768\u6c0f\u6a21\u91cf\u5927\u7ea6\u4e3a 2.01e11N\/m^2\uff0c\u94dc\u7684\u662f 1.1e11 N\/m^2\u3002<\/p>\n\n\n\n

**(2) \u5f39\u6027\u6a21\u91cf **E(Elastic Modulus)\uff1a<\/strong><\/p>\n\n\n\n

\u5f39\u6027\u6a21\u91cf E \u662f\u6307\u6750\u6599\u5728\u5f39\u6027\u53d8\u5f62\u8303\u56f4\u5185 (\u5373\u5728\u6bd4\u4f8b\u6781\u9650\u5185)\uff0c\u4f5c\u7528\u4e8e\u6750\u6599\u4e0a\u7684\u7eb5\u5411\u5e94\u529b\u4e0e\u7eb5\u5411\u5e94\u53d8\u7684\u6bd4\u4f8b\u5e38\u6570\u3002\u4e5f\u5e38\u6307\u6750\u6599\u6240\u53d7\u5e94\u529b\u5982\u62c9\u4f38\uff0c\u538b\u7f29\uff0c\u5f2f\u66f2\uff0c\u626d\u66f2\uff0c\u526a\u5207\u7b49) \u4e0e\u6750\u6599\u4ea7\u751f\u7684\u76f8\u5e94\u5e94\u53d8\u4e4b\u6bd4\u3002\u5f39\u6027\u6a21\u91cf\u662f\u8868\u5f81\u6676\u4f53\u4e2d\u539f\u5b50\u95f4\u7ed3\u5408\u529b\u5f3a\u5f31\u7684\u7269\u7406\u91cf\uff0c\u6545\u662f\u7ec4\u7ec7\u7ed3\u6784\u4e0d\u654f\u611f\u53c2\u6570\u3002\u5728\u5de5\u7a0b\u4e0a\uff0c\u5f39\u6027\u6a21\u91cf\u5219\u662f\u6750\u6599\u521a\u5ea6\u7684\u5ea6\u91cf\uff0c\u662f\u7269\u4f53\u53d8\u5f62\u96be\u6613\u7a0b\u5ea6\u7684\u8868\u5f81\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e\u67d0\u4e9b\u6750\u6599\u5728\u5f39\u6027\u8303\u56f4\u5185\u5e94\u529b – \u5e94\u53d8\u66f2\u7ebf\u5e76\u4e0d\u7b26\u5408\u76f4\u7ebf\u5173\u7cfb\u7684\uff0c\u5219\u53ef\u6839\u636e\u9700\u8981\u53d6\u5207\u7ebf\u5f39\u6027\u6a21\u91cf\u3001\u5272\u7ebf\u5f39\u6027\u6a21\u91cf\u7b49\u4eba\u4e3a\u5b9a\u4e49\u7684\u529e\u6cd5\u6765\u4ee3\u66ff\u5b83\u7684\u5f39\u6027\u6a21\u91cf\u503c\u3002\u6839\u636e\u4e0d\u540c\u7684\u53d7\u529b\u60c5\u51b5\uff0c\u5206\u522b\u6709\u76f8\u5e94\u7684\u62c9\u4f38\u5f39\u6027\u6a21\u91cf modulus of elasticity for tension (\u6768\u6c0f\u6a21\u91cf)\u3001\u526a\u5207\u5f39\u6027\u6a21\u91cf shearmodulus of elasticity (\u521a\u6027\u6a21\u91cf)\u3001\u4f53\u79ef\u5f39\u6027\u6a21\u91cf\u3001\u538b\u7f29\u5f39\u6027\u6a21\u91cf\u7b49\u3002<\/p>\n\n\n\n

(3) \u526a\u5207\u6a21\u91cf G(Shear Modulus)\uff1a<\/strong><\/p>\n\n\n\n

\u526a\u5207\u6a21\u91cf\u662f\u6307\u526a\u5207\u5e94\u529b\u4e0e\u526a\u5207\u5e94\u53d8\u4e4b\u6bd4\u3002\u526a\u5207\u6a21\u6570 G = \u526a\u5207\u5f39\u6027\u6a21\u91cf G = \u5207\u53d8\u5f39\u6027\u6a21\u91cf G\u3002\u5b83\u662f\u6750\u6599\u7684\u57fa\u672c\u7269\u7406\u7279\u6027\u53c2\u6570\u4e4b\u4e00\uff0c\u4e0e\u6768\u6c0f (\u538b\u7f29\u3001\u62c9\u4f38) \u5f39\u6027\u6a21\u91cf E\u3001\u6cca\u6851\u6bd4\u03bd\u5e76\u5217\u4e3a\u6750\u6599\u7684\u4e09\u9879\u57fa\u672c\u7269\u7406\u7279\u6027\u53c2\u6570\uff0c\u5728\u6750\u6599\u529b\u5b66\u3001\u5f39\u6027\u529b\u5b66\u4e2d\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002<\/p>\n\n\n\n

\u5176\u5b9a\u4e49\u4e3a\uff1aG=\u03c4\/\u03b3\uff0c \u5176\u4e2d G(Mpa) \u4e3a\u5207\u53d8\u5f39\u6027\u6a21\u91cf\uff1b\u03c4\u4e3a\u526a\u5207\u5e94\u529b (MPa)\uff1b\u03b3\u4e3a\u526a\u5207\u5e94\u53d8 (\u5f27\u5ea6)\u3002<\/p>\n\n\n\n

(4) \u4f53\u79ef\u6a21\u91cf K(Bulk Modulus)\uff1a<\/strong><\/p>\n\n\n\n

\u4f53\u79ef\u6a21\u91cf\u53ef\u63cf\u8ff0\u5747\u8d28\u5404\u5411\u540c\u6027\u56fa\u4f53\u7684\u5f39\u6027\uff0c\u53ef\u8868\u793a\u4e3a\u5355\u4f4d\u9762\u79ef\u7684\u529b\uff0c\u8868\u793a\u4e0d\u53ef\u538b\u7f29\u6027\u3002\u516c\u5f0f\u5982\u4e0b K=E\/(3\u00d7(1-2*v))\uff0c\u5176\u4e2d E \u4e3a\u5f39\u6027\u6a21\u91cf\uff0cv \u4e3a\u6cca\u677e\u6bd4\u3002\u5177\u4f53\u53ef\u53c2\u8003\u5927\u5b66\u91cc\u7684\u4efb\u4e00\u672c\u5f39\u6027\u529b\u5b66\u4e66\u3002<\/p>\n\n\n\n

\u6027\u8d28\uff1a\u7269\u4f53\u5728 p0 \u7684\u538b\u529b\u4e0b\u4f53\u79ef\u4e3a V0\uff0c\u82e5\u538b\u529b\u589e\u52a0 (p0\u2192p0+dP)\uff0c\u5219\u4f53\u79ef\u51cf\u5c0f\u4e3a (V0-dV)\u3002\u5219\u88ab\u79f0\u4e3a\u8be5\u7269\u4f53\u7684\u4f53\u79ef\u6a21\u91cf (modulus of volume elasticity)\u3002\u5982\u5728\u5f39\u6027\u8303\u56f4\u5185\uff0c\u5219\u4e13\u79f0\u4e3a\u4f53\u79ef\u5f39\u6027\u6a21\u91cf\u3002\u4f53\u79ef\u6a21\u91cf\u662f\u4e00\u4e2a\u6bd4\u8f83\u7a33\u5b9a\u7684\u6750\u6599\u5e38\u6570\u3002\u56e0\u4e3a\u5728\u5404\u5411\u5747\u538b\u4e0b\u6750\u6599\u7684\u4f53\u79ef\u603b\u662f\u53d8\u5c0f\u7684\uff0c\u6545 K \u503c\u6c38\u4e3a\u6b63\u503c\uff0c\u5355\u4f4d MPa\u3002\u4f53\u79ef\u6a21\u91cf\u7684\u5012\u6570\u79f0\u4e3a\u4f53\u79ef\u67d4\u91cf\u3002\u4f53\u79ef\u6a21\u91cf\u548c\u62c9\u4f38\u6a21\u91cf\u3001\u6cca\u677e\u6bd4\u4e4b\u95f4\u6709\u5173\u7cfb\uff1aE=3K(1-2\u03bc)\u3002<\/p>\n\n\n\n

(5) \u538b\u7f29\u6a21\u91cf (Compression Modulus)\uff1a<\/strong><\/p>\n\n\n\n

\u7269\u4f53\u5728\u53d7\u4e09\u8f74\u538b\u7f29\u65f6\u538b\u5e94\u529b\u4e0e\u538b\u7f29\u5e94\u53d8\u7684\u6bd4\u503c\u3002\u5b9e\u9a8c\u4e0a\u53ef\u7531\u5e94\u529b – \u5e94\u53d8\u66f2\u7ebf\u8d77\u59cb\u6bb5\u7684\u659c\u7387\u786e\u5b9a\u3002\u5f84\u5411\u540c\u6027\u6750\u6599\u7684\u538b\u7f29\u6a21\u91cf\u503c\u5e38\u4e0e\u5176\u6768\u6c0f\u6a21\u91cf\u503c\u8fd1\u4f3c\u76f8\u7b49\u3002<\/p>\n\n\n\n

\u571f\u7684\u538b\u7f29\u6a21\u91cf\u6307\u5728\u4fa7\u9650\u6761\u4ef6\u4e0b\u571f\u7684\u5782\u76f4\u5411\u5e94\u529b\u4e0e\u5e94\u53d8\u4e4b\u6bd4\uff0c\u662f\u901a\u8fc7\u5ba4\u5185\u8bd5\u9a8c\u5f97\u5230\u7684\uff0c\u662f\u5224\u65ad\u571f\u7684\u538b\u7f29\u6027\u548c\u8ba1\u7b97\u5730\u57fa\u538b\u7f29\u53d8\u5f62\u91cf\u7684\u91cd\u8981\u6307\u6807\u4e4b\u4e00\u3002\u538b\u7f29\u6a21\u91cf\u8d8a\u5927\uff0c\u571f\u8d8a\u575a\u786c\u3002<\/p>\n\n\n\n

(6) \u50a8\u80fd\u6a21\u91cf Es\uff1a<\/strong><\/p>\n\n\n\n

\u50a8\u80fd\u6a21\u91cf Es \u5b9e\u8d28\u4e3a\u6768\u6c0f\u6a21\u91cf\uff0c\u8868\u8ff0\u6750\u6599\u5b58\u50a8\u5f39\u6027\u53d8\u5f62\u80fd\u91cf\u7684\u80fd\u529b\u3002\u50a8\u80fd\u6a21\u91cf\u8868\u5f81\u7684\u662f\u6750\u6599\u53d8\u5f62\u540e\u56de\u5f39\u7684\u6307\u6807\u3002\u50a8\u80fd\u6a21\u91cf E\\’\u662f\u6307\u7c98\u5f39\u6027\u6750\u6599\u5728\u4ea4\u53d8\u5e94\u529b\u4f5c\u7528\u4e0b\u4e00\u4e2a\u5468\u671f\u5185\u50a8\u5b58\u80fd\u91cf\u7684\u80fd\u529b\uff0c\u901a\u5e38\u6307\u5f39\u6027\u3002\u590d\u6570\u6a21\u91cf\u7684\u5b9e\u6570\u90e8\u5206\uff0c\u8868\u793a\u9ecf\u5f39\u6027\u6750\u6599\u5728\u5f62\u53d8\u8fc7\u7a0b\u4e2d\u7531\u4e8e\u5f39\u6027\u5f62\u53d8\u800c\u50a8\u5b58\u7684\u80fd\u91cf\u3002<\/p>\n\n\n\n

(7) \u8017\u80fd\u6a21\u91cf Ei\uff1a<\/strong><\/p>\n\n\n\n

\u8017\u80fd\u6a21\u91cf Ei \u662f\u6a21\u91cf\u4e2d\u5e94\u529b\u4e0e\u53d8\u5f62\u5f02\u6b65\u7684\u7ec4\u5143\uff1b\u7528\u6765\u8868\u5f81\u6750\u6599\u8017\u6563\u53d8\u5f62\u80fd\u91cf\u7684\u80fd\u529b, \u4f53\u73b0\u4e86\u6750\u6599\u7684\u7c98\u6027\u672c\u8d28\u3002\u5b83\u8868\u793a\u5f53\u6750\u6599\u53d1\u751f\u5f62\u53d8\u65f6\uff0c\u80fd\u91cf\u8f6c\u5316\u6210\u70ed\u80fd\u7684\u963b\u5c3c\u672f\u8bed\uff0c\u662f\u590d\u6742\u6a21\u578b\u7684\u4e00\u4e2a\u7b80\u5355\u90e8\u5206\uff0c\u662f\u4ece\u80fd\u91cf\u635f\u8017\u7684\u89d2\u5ea6\u5bf9 \u201c\u50a8\u80fd\u6a21\u91cf\u201d \u8fdb\u884c\u5206\u6790\u800c\u4ea7\u751f\u7684\u672f\u8bed\u3002\u8017\u80fd\u6a21\u91cf Ei \u6307\u7684\u662f\u5728\u4e00\u4e2a\u53d8\u5316\u5468\u671f\u5185\u6240\u6d88\u8017\u80fd\u91cf\u7684\u80fd\u529b\u3002<\/p>\n\n\n\n

(8) \u5207\u7ebf\u6a21\u91cf (Tangent Modulus)\uff1a<\/strong><\/p>\n\n\n\n

\u5207\u7ebf\u6a21\u91cf\u5c31\u662f\u5851\u6027\u9636\u6bb5\uff0c\u5c48\u670d\u6781\u9650\u548c\u5f3a\u5ea6\u6781\u9650\u4e4b\u95f4\u7684\u66f2\u7ebf\u659c\u7387\u3002\u662f\u5e94\u529b\u5e94\u53d8\u66f2\u7ebf\u4e0a\u5e94\u529b\u5bf9\u5e94\u53d8\u7684\u4e00\u9636\u5bfc\u6570\u3002\u5176\u5927\u5c0f\u4e0e\u5e94\u529b\u6c34\u5e73\u6709\u5173\uff0c\u5e76\u975e\u4e00\u5b9a\u503c\u3002\u5207\u7ebf\u6a21\u91cf\u4e00\u822c\u7528\u4e8e\u589e\u91cf\u6709\u9650\u5143\u8ba1\u7b97\u3002\u5207\u7ebf\u6a21\u91cf\u548c\u5c48\u670d\u5e94\u529b\u7684\u5355\u4f4d\u90fd\u662f N\/m^2\u3002<\/p>\n\n\n\n

(9) \u622a\u9762\u6a21\u91cf\uff1a<\/strong><\/p>\n\n\n\n

\u622a\u9762\u6a21\u91cf\u662f\u6784\u4ef6\u622a\u9762\u7684\u4e00\u4e2a\u529b\u5b66\u7279\u6027\u3002\u662f\u8868\u793a\u6784\u4ef6\u622a\u9762\u62b5\u6297\u67d0\u79cd\u53d8\u5f62\u80fd\u529b\u7684\u6307\u6807\uff0c\u5982\u6297\u5f2f\u622a\u9762\u6a21\u91cf\u3001\u6297\u626d\u622a\u9762\u6a21\u91cf\u7b49\u3002\u5b83\u53ea\u4e0e\u622a\u9762\u7684\u5f62\u72b6\u53ca\u4e2d\u548c\u8f74\u7684\u4f4d\u7f6e\u6709\u5173\uff0c\u800c\u4e0e\u6750\u6599\u672c\u8eab\u7684\u6027\u8d28\u65e0\u5173\u3002\u5728\u6709\u4e9b\u4e66\u4e0a\uff0c\u622a\u9762\u6a21\u91cf\u53c8\u79f0\u4e3a\u622a\u9762\u7cfb\u6570\u6216\u622a\u9762\u62b5\u6297\u77e9\u7b49\u3002<\/p>\n\n\n\n

(10) \u590d\u5408\u6a21\u91cf\uff08E*\uff0ccomplex modulus\uff09<\/strong><\/p>\n\n\n\n

\u590d\u5408\u6a21\u91cf\u5305\u62ec\u50a8\u80fd\u6a21\u91cf Es \u548c\u635f\u8017\u6a21\u91cf Ei\uff0c\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u4e3a\uff1a<\/p>\n\n\n\n

Es=E*cos\u03b4<\/p>\n\n\n\n

El=E*sin\u03b4 <\/p>\n\n\n\n

|E*|=sqrt(Es^2+El^2)<\/p>\n\n\n\n

\u6765\u6e90\uff1a\u6cca\u677e\u6bd4<\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

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