Layout optimization of junctions yields the minimum number of junctions. And a fewer junctions means fewer joint components or fewer spot-welding operations, and this leads to higher production efficiency. A method is developed for optimizing the layout of junctions between two structures so as to minimize the relative displacement between them when one of them is oscillated by noise disturbances. A quadratic response function serves as the expected value of relative displacement between the two structures and as the objective function in the optimization process. A set of evenly distributed variable-spring elements joins the two solid structures in a single junction surface, and the distribution of elasticity indices is continually revised. After optimization, those spring elements with elasticity indices higher than a certain threshold are considered to represent rigid joints, while lower elasticity indices indicate the absence of any joints. The optimized elasticity-index distribution thus shows where to place junctions. Use of variable-strength spring joints like this makes it easier to determine optimum junction positions. This is because it eliminates the need to renew the entire FEM model for each case.