Real-time physics simulation has been extensively used in computer games, but its potential has yet to be fully realized in design and education. We present an interactive 3D physics engine with a wide variety of applications. In common with traditional FEM, the use of a local element stiffness matrix is retained. However, unlike typical non-linear FEM routines elements forces, moments and inertia are appropriately lumped at nodes following the dynamic relaxation method. A semi-implicit time integration scheme updates linear and angular momentum, and subsequently the local coordinate frames of the nodes. A co-rotational approach is used to compute the resultant field of displacements in global coordinates including the effect of large deformations. The results obtained compare well against established commercial software. We demonstrate that the method presented allows the making of interactive structural models that can be used in teaching to develop an intuitive understanding of structural behaviour. We also show that the same interactive physics framework allows real-time optimization that can be used for geometric and structural design applications.