The designs of on-board electronic devices used in automobiles need to satisfy not only electronic requirements but also physical requirements such maintaining sufficient stiffness under loads. The development of multi-disciplinary optimization methods that also handle multi-physics issues can facilitate a systematic approach to the design of such devices. In this study, we propose a new multi-disciplinary topology optimization method that handles multi-physics phenomena, namely, the coupling of electromagnetic wave propagation problems with static structural mechanics problems. The Finite Difference-Time Domain method is used to solve the electromagnetic wave propagation problem, while the static structural mechanics problem is solved using the Finite Element Method. New relaxation schemes for the design domain and design variable settings are proposed to deal with the use of the different numerical methods. The integral reflection electric energy and the mean compliance are formulated as objective functions to be minimized in an optimization problem. A multi-objective function is also formulated based on a weighted sum formulation to deal with the two objective functions. The optimization algorithm is constructed based on sequential linear program-ming. A design example of a multiple-band dielectric resonator antenna is provided to show the usefulness of the proposed method.