The paper by M.P. Bendsøe discusses the optimal shape design problem as a material distribution problem, aiming to determine the optimal spatial material distribution for given loads and boundary conditions. The traditional discrete nature of the problem, where each point in space is either a material point or a void, is addressed by introducing a density function as a continuous design variable. This approach allows for the definition of high-density regions that define the shape of the mechanical element, while intermediate densities can be handled using artificial material laws or homogenization techniques. The paper highlights the limitations of boundary variation techniques, which are limited to predicting the optimal shape of boundaries within a given topology. It proposes a new method that can determine both the optimal topology and shape of a structure, making it a useful extension of current methodologies. The formulation of the problem is presented in a general setting, similar to sizing problems, and the energy bilinear form and load linear form are introduced to formulate the minimum compliance problem. The paper also compares different composite materials and artificial laws to demonstrate the effectiveness of the proposed methods in determining the topology and shape of mechanical elements.The paper by M.P. Bendsøe discusses the optimal shape design problem as a material distribution problem, aiming to determine the optimal spatial material distribution for given loads and boundary conditions. The traditional discrete nature of the problem, where each point in space is either a material point or a void, is addressed by introducing a density function as a continuous design variable. This approach allows for the definition of high-density regions that define the shape of the mechanical element, while intermediate densities can be handled using artificial material laws or homogenization techniques. The paper highlights the limitations of boundary variation techniques, which are limited to predicting the optimal shape of boundaries within a given topology. It proposes a new method that can determine both the optimal topology and shape of a structure, making it a useful extension of current methodologies. The formulation of the problem is presented in a general setting, similar to sizing problems, and the energy bilinear form and load linear form are introduced to formulate the minimum compliance problem. The paper also compares different composite materials and artificial laws to demonstrate the effectiveness of the proposed methods in determining the topology and shape of mechanical elements.