Abstract:Elastic modulus is an important performance parameter of engineering materials, which can measure the ability of an object to resist elastic deformation. Elastography is a medical imaging method that characterizes the physical properties of biological tissues through elastic modulus. To apply the elastography method to the damage identification of mechanical equipment structures and improve the local characterization and the global identification capabilities of elastography, a structural elastography method based on the topology optimization method is proposed. Inspired by the topology optimization theory, the relative densities or elastic modulus coefficients of the discrete elements of the structure are used as the elastography parameters to characterize the degree of damage. The interpolation model of imaging parameters and elastic modulus is then established. The mapping relationship between damage characterization, structural model, and physical response is constructed based on the finite element model. The least-square of the displacement responses of the damaged structure and the undamaged structure is taken as the optimization objective function. The upper and lower limits of imaging parameters are taken as constraints. The optimization model of the structural elastography is established based on the objective and constraints. The sensitivity of the imaging problem is derived based on the adjoint method. The numerical implementation for the inverse solution of the elastography problem is given in detail. Two 2D cantilever beam and Michell beam numerical examples are firstly conducted. The imaging results show that the topology optimization based elastography method can obtain high-quality elastic modulus images of structures with homogeneous and heterogeneous materials without any prior information. The elastography method is also effective for the imaging of structures with single damage and multi-damages. And the imaging results do not depend on specific boundary conditions. The elastography method is further extended to a 3D cantilever beam problem to verify the generalization of the proposed method.