We show that conventional finite element technology can be applied to topology optimization of 2D and 3D continua. Nodal design variables, classical Newton-Raphson solution for the first-order KKT equations and the screened-Poisson equation are sufficient to produce smooth results without the use of level-sets or phase-field technologies. Side-constraints are addressed with variable transformation and a single Lagrange multiplier enforces the volume constraint. We also use our mesh-division Algorithm specialized to topology optimization as a form of producing compatible meshes. By means of 2D and 3D numerical experimentation, we make the case for this approach to density-based compliance minimization. Verification examples are shown, with the corresponding compliance and volume evolution exhibiting a sound behavior.

我们表明，传统的有限元技术可以应用于2D和3D连续体的拓扑优化。节点设计变量，一阶KKT方程的经典Newton-Raphson解和屏蔽Poisson方程足以产生平滑的结果，而无需使用电平集或相场技术。侧面约束通过变量转换解决，并且单个Lagrange乘数强制执行体积约束。我们还使用专门用于拓扑优化的网格划分算法，作为生成兼容网格的一种形式。通过2D和3D数值实验，我们为这种基于密度的依从性最小化的方法提供了理由。显示了验证示例，相应的依从性和体积演变表现出良好的行为。