The paper presents an efficient 88 line MATLAB code for topology optimization. It has been developed using the 99 line code presented by Sigmund (Struct Multidisc Optim 21(2):120-127, 2001) as a starting point. The original code has been extended by a density filter, and a considerable improvement in efficiency has been achieved, mainly by preallocating arrays and vectorizing loops. A speed improvement with a factor of 100 is obtained for a benchmark example with 7,500 elements. Moreover, the length of the code has been reduced to a mere 88 lines. These improvements have been accomplished without sacrificing the readability of the code. The 88 line code can therefore be considered as a valuable successor to the 99 line code, providing a practical instrument that may help to ease the learning curve for those entering the field of topology optimization. The paper also discusses simple extensions of the basic code to include recent PDE-based and black-and-white projection filtering methods

WTclient.dll，是一个OPC客户端开发工具，收费的，大概900多美元。如果不授权，基本连接30分钟就要断开。先破解修改为时间限制为99年

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本代码是作者为了方便拓扑优化初学者尽快入门而制作的，在原99行代码的基础上详细注释了每行代码的程序翻译，并与《A 99 line topology optimization code written in Matlab》O. Sigmund 原文公式进行对照标注。

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