Analytic formulas of energy release rates for delamination using a global–local method

This article presents analytic solutions of energy release rates of a cracked laminate by using a global–local method. Deformations of a cracked laminate subjected to pure bending moments are analyzed and then a new mode partition equation is proposed. By using this partition equation, closed-form solutions of energy release rates G_I and G_II are derived by using a global method. For a cracked laminate subjected to axial forces and bending moments, a local method based on the crack-tip force model is used and the unknown coefficient is solved by combining the present analytic solutions for the bending moment loading case. Numerical results of the mode mixity predicted by the present closed-form formulations correlate well with those numerically calibrated on the basis of the singular field and crack-tip force models.     

Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature.     

An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band

Nonlinear Dynamics - Quasi-zero stiffness (QZS) isolators can achieve superior performance in vibration isolation; however, this superiority is often effective only for an excitation with the small...     

Constitutive equations for 0-3 polarized PLZT actuators

This article presents constitutive equations of transparent lead lanthanum zirconate titanate (PLZT) materials poling along thickness direction or with 0-3 polarization. Discussed first are the Beer’s law of light transmission in transparent solid and the photovoltaic current density in PLZT materials. Formulas for field strength and electrical potential between two electrodes of a PLZT wafer are then derived from the basic photovoltaic equations. By superposing the photovoltaic and the converse piezoelectric effects, we formulate a novel expression for photo-induced strain that is nonlinearly dependent of incident light intensity and varies with light penetration depth in through-thickness direction. On the basis of the derived photo-induced strain, linear and nonlinear constitutive equations of 0-3 polarized PLZT actuators are formulated. The present model is validated by using the available experimental data in the literature. By using the present model with an exponential variation of strain through the thickness, closed-form solutions for the equivalent loads acting on a PLZT unimorph, bimorph and intelligent beam are obtained and then compared with numerical results available in the literature.     

A variational principle and finite element formulation for multi-physics PLZT ceramics

This research presents an extended variational principle and a finite element formulation for multi-physics analysis of PLZT (lanthanum zirconate titanate) ceramics by including the photovoltaic and optothermic effects. The photo-induced electrical and thermal, and mechanical fields, as well as the heat source effect due to light illumination are all considered in the formulation. A generalized variation approach for advanced multi-physics PLZT problems is developed and then the relevant finite element formulation is established.     

Multi-physics field models of photostrictive unimorphs and heterogeneous bimorphs subjected to light illumination and mechanical loading

This paper presents novel constituent equations for photostrictive unimorphs and heterogeneous bimorphs by considering multi-physics fields. Although the formulation is conducted using the lead lanthanum zirconate titanate ceramics (PLZT) polarized in 0-3 direction subjected to light illumination and mechanical loading, the results may be extended to other photostrictive materials or degenerated to piezoelectric ceramics. In the present formulation, photo-induced electrical, thermal and mechanical fields in PLZT ceramics are studied first, and then one-dimensional opto-thermo-piezoelectric equations for 0-3 polarized PLZT and other photostrictive materials are discussed. On the basis of the photo-induced multi-physics equations, 0-3 polarized PLZT unimorphs and bimorphs are investigated and the associated constituent equations are derived. The numerical results calculated using the present formulations are then compared with those available in the literatures to validate the derived novel constituent equations.