Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional,linear,second-order,boundary value problems with a domain completely described by a circular defining curve.The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems,bounded and unbounded bodies,distributed body source,and.general boundary conditions to be treated in a unified fashion.The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve,exact geometry of the domain,and exact spatial differential operators.Standard finite element shape functions are employed in the discretization of both trial and test functions in the circumferential direction and the resulting eigenproblem is solved by a selected efficient algorithm.The computational performance of the implemented procedure is then fully investigated for various scenarios to demonstrate the accuracy in comparison with standard linear elements.

Investigation of Generalized SIFs of cracks in 3D piezoelectric media under various crack-face conditions

This paper investigates the influence of crack geometry,crack-face and loading conditions,and the permittivity of a medium inside the crack gap on intensity factors of planar and non-planar cracks in linear piezoelectric media.A weakly singular boundary integral equation method together with the near-front approximation is adopted to accurately determine the intensity factors.Obtained results indicate that the non-flat crack surface,the electric field,and the permittivity of a medium inside the crack gap play a crucial role on the behavior of intensity factors.The mode-I stress intensity factors(K1)for two representative non-planar cracks under different crack-face conditions are found significantly different and they possess both upper and lower bounds.In addition,K1 for impermeable and semi-permeable non-planar cracks treated depends strongly on the electric field whereas those of impermeable,permeable,and semi-permeable penny-shaped cracks are identical and independent of the electric field.The stress/electric intensity factors predicted by permeable and energetically consistent models are,respectively,independent of and dependent on the electric field for the penny-shaped crack and the two representative non-planar cracks.Also,the permittivity of a medium inside the crack gap strongly affects the intensity factors for all crack configurations considered except for K1 of the semi-permeable pennyshaped crack.

Size effects in two-dimensional layered materials modeled by couple stress elasticity

In the present study,the effect of material microstructure on the mechanical response of a two-dimensional elastic layer perfectly bonded to a substrate is examined under surface loadings.In the current model,the substrate is treated as an elastic half plane as opposed to a rigid base,and this enables its applications in practical cases when the modulus of the layer(e.g.,the coating material)and substrate(e.g.,the coated surface)are comparable.The material microstructure is modeled using the generalized continuum theory of couple stress elasticity.The boundary value problems are formulated in terms of the displacement field and solved in an analytical manner via the Fourier transform and stiffness matrix method.The results demonstrate the capability of the present continuum theory to efficiently model the size-dependency of the response of the material when the external and internal length scales are comparable.Furthermore,the results indicated that the material mismatch and substrate stiffness play a crucial role in the predicted elastic field.Specifically,the study also addresses significant discrepancy of the response for the case of a layer resting on a rigid substrate.