Fig. 1 Flowchart of the optimization procedure ate since they require a large number of full model analyses whileapriori indicators are generally far more efficient in terms of computational time. Elastic strain energy of the elements is assumed to be very closely linked with the eigenfrequency shift, thus we decide to use a priori indicator based on elastic strain energy in spot weld and its adjacent shell elements. Additionally, the energy is normalized by the volume of the adjacent shell elements in order to remove the effect of their varying sizes. The indicator value for ithspot weld for modek canbe expressed as: Ii,k =UT k K e,iUk +UT k K sh,iUk Vsh,i m Vsh,i tot , (1) where Ke,i is the stiffness matrix of ith RSW, Ksh,i is the stiffness matrix of shell elements adjacent to ithRSW, Uk is the eigenvector k whileV sh,i m andV sh,i tot are Q. I. Bhatti and M. Ouisse and S. Cogan 300
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