Topology optimization generates optimal designs for specified loads. This includes designs with minimal mass subject to a constraint on a system response, such as deformation. Many loading scenarios, and, thus, many constraints on the system response can make topology optimization expensive. This is relevant, e.g., under uncertain loading conditions. Similarly, in optimization problems subject to constraints on the total eigenfrequency, many vibrational modes have to be considered. For these problems, it is beneficial to formulate constraints on the stiffness of the structure rather than on its response to individual loads. In the approach, introduced by Frank et al. and Frank and Zimmermann, this is done using a so-called interface stiffness matrix (or similarly its inverse, a compliance matrix). More specifically the lowest eigenvalue of the so-called stiffness excess matrix, i.e., the difference between the interface stiffness matrix and a limit matrix, are subject to the constraint to be positive to ensure sufficient overall stiffness. In this paper we present (1) a motivation of a meaningful limit stiffness matrix for many loads, and (2) an algorithm to solve the topology optimization problem subject to the eigenvalue constraint to ensure sufficient stiffness.