Efficient time-domain spectral element with zigzag kinematics for multilayered strips. (15th October 2022)

• Record Type: Journal Article
• Authors: Jain, Mayank; Kapuria, Santosh; Pradyumna, S.
• Is Part Of: International journal of mechanical sciences. Volume 232(2022)
• Publication Date: 2022-10-15
• Subjects: Spectral element -- C1-continuous spectral interpolation -- Zigzag theory -- Lamb wave propagation -- Structural health monitoring -- Laminated composite -- Fiber-metal laminate; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2022.107603
• Languages: English
• ISSNs: 0020-7403

Abstract

Abstract: Efficient structural elements are widely sought for fast computation of wave propagation response of anisotropic multilayered structures for their design, non-destructive testing, and structural health monitoring purposes. Although zigzag theories are known to combine excellent accuracy with high computational efficiency, no spectral element has been developed so far based on these theories, which would enable fast and accurate simulation of guided waves in such structures. In this article, we develop an efficient time-domain spectral strip element for analyzing ultrasonic wave propagation in multi-material laminated beams and panels while accounting for the zigzag profile of the in-plane displacement across the thickness. The theory superimposes a layerwise linear (zigzag) variation of the in-plane displacement of a layerwise theory onto the global third-order variation of an equivalent single layer (ESL) third-order theory while retaining the computational advantage of the latter. The high-order element has an arbitrary number of unequally spaced nodes with only four kinematic variables at each node, regardless of the number of laminas. The recently proposed generalized Hermite-type C 1 -continuous Lobatto shape functions interpolate the deflection, while the axial displacement and shear rotation are interpolated using the C 0 -continuous Lobatto shape functions. A comprehensive numerical study establishes high efficiency, excellent accuracy, and fast convergence of the new element in analyzing free vibration and guided wave propagation in single-material composite and multi-material fiber-metal laminate structures. Its combined performance in terms of these parameters is much superior to its standard FE counterpart, the ESL theory-based elements, and the continuum elements in the considered frequency range. Graphical abstract: Highlights: Time-domain spectral element based on a zigzag laminate theory developed for the first time. Considers interfacial slope discontinuities of the in-plane displacement. Employs C 1 -continuous Lobatto basis functions for interpolating deflection. Yields excellent accuracy with a multi-fold reduction in computing time from standard FE. Useful for guided wave-based structural health monitoring of multi-material laminated structures.