Failure of adhesively bonded joints is often dictated by the stresses developed within the adhesive layer, which are difficult to measure experimentally. While solutions, including closed-form solutions, exist for static cases, even numerical solutions are not easily obtainable for dynamic cases where the bonded layers are dissimilar in material and/or geometry. In this paper, we present a method to determine the dynamic stresses in the adhesive and adherends of adhesively bonded lap joints subjected to arbitrary dynamic end loads. In the formulation the adherends are treated as orthotropic plates while the adhesive layer is approximated as a tension-shear spring. The equations of motion result in a complex system of fourteen (14) partial differential equations in time and space. The equations are solved numerically using the Finite Difference Method (FDM). First, special cases where known solutions exist are solved to verify both the formulation and the numerical approach. Next, the problem of a lap joint subject to a remote, transmitted impact is considered and results are obtained. The planar distribution of stresses within the adhesive layer shows areas of dynamic stress concentration which may act as crack nucleation sites.

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