Maenghyo Cho

An efficient higher-order plate theory for laminated composites

Abstract An efficient higher-order plate theory for laminated composites is developed. The theory for symmetric laminated composites is obtained by superposing a cubic varying displacement field on a zig-zag linearly varying displacement. The theory has the same number of dependent unknowns as first-order shear deformation theory, and the number of unknowns is independent of the number of layers. The displacement satisfies transverse shear stress continuity conditions at the interface between layers as well as shear free surface conditions. Thus an artificial shear correction factor is not needed. To demonstrate and compare with other theories, the analytical solution for cylindrical bending is obtained. The present theory gives deflections and stresses which compare well with other known theories.

Higher-Order Zig-Zag Theory for Laminated Composites With Multiple Delaminations

A higher-order zig-zag theory has been developed for laminated composite plates with multiple delaminations. By imposing top and bottom surface transverse shear stress-free conditions and interface continuity conditions of transverse shear stresses including delaminated interfaces, the displacement field with minimal degree-of-freedoms are obtained. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Through the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. The delaminated beam finite element is implemented to evaluate the performance of the newly developed theory. Linear buckling and natural frequency analysis demonstrate the accuracy and efficiency of the present theory. The present higher-order zig-zag theory should work as an efficient tool to analyze the static and dynamic behavior of the composite plates with multiple delaminations.

FINITE ELEMENT FOR COMPOSITE PLATE BENDING BASED ON EFFICIENT HIGHER ORDER THEORY

A triangular bending element based on an efficient higher order plate theory is developed for symmetric laminated composites. This nonconforming element has five degrees of freedom in each node. It passes proper bending and shear patch tests in arbitrary meshes in isotropic materials. Thus it converges to the exact solution. To demonstrate the element and compare with other theories, finite element solutions are obtained for a static bending problem under sinusoidal loading. The present finite element results give deflections and stresses that are in good agreement with three-dimensional elasticity solutions. Thus this element provides an efficient and accurate tool for the analysis of symmetric multilayered composite plates

Iterative free-edge stress analysis of composite laminates under extension, bending, twisting and thermal loadings

An iterative method has been applied to analyze free edge interlaminar stresses of composite laminates which are subject to extension, bending, twisting and thermal loads. The stresses, which satisfy the traction-free conditions not only at the free edges but also at the top and bottom surfaces of laminates, are obtained by using the complementary virtual work and the extended Kantorovich method. In order to obtain accurate interlaminar stresses, static and kinematic continuity conditions are applied at the interfaces between plies through iterations. To demonstrate the validity of the proposed method, cross-ply, angle-ply, and quasi-isotropic laminates are considered. Through the iteration processes, the convergence of the solutions is demonstrated. The present method provides accurate stresses in the interior and near the free edges of laminates. It can be utilized as an analytical tool to predict interlaminar stresses under the loads of mechanical and thermal combined.

Higher order zig-zag plate theory under thermo-electric-mechanical loads combined

A higher order zig-zag plate theory is developed to refine the predictions of the mechanical, thermal, and electric behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Artificial shear correction factors are not needed in the present formulation. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick smart composite plate under mechanical, thermal, and electric loads combined.

A Study on the Room-Temperature Curvature Shapes of Unsymmetric Laminates Including Slippage Effects

The room-temperature shapes of cured unsymmetric composite laminates have out-of-plane warping after autoclave processing. In addition, they exhibit two stable room-temperature configurations due to snap-through phenomena when the side length of laminates exceed a critical value. The cured shape of unsymmetric laminates are influenced by many factors. Experiments show that the effect of tool-plate cannot be ignored and has significant influence on the cured shape. This study examines slippage effects resulting from the interaction between the laminates and the tool-plate which are ignored in the previous researches. By introducing a dimensionless slippage coefficient and correlating the corresponding value with experimental results, the influence of processing parameters is investigated. Modeling is extended to predict curvatures of general lamination layup configurations.

Engineering design framework for a shape memory alloy coil spring actuator using a static two-state model

A shape memory alloy (SMA) coil spring actuator is fabricated by annealing an SMA wire wound on a rod. Four design parameters are required for the winding: the wire diameter, the rod diameter, the pitch angle and the number of active coils. These parameters determine the force and stroke produced by the actuator. In this paper, we present an engineering design framework to select these parameters on the basis of the desired force and stoke. The behavior of the SMA coil spring actuator is described in detail to provide information about the inner workings of the actuator and to aid in selecting the design parameters. A new static two-state model, which represents a force?deflection relation of the actuator at the fully martensitic state (M100%) and fully austenitic state (A100%), is derived for use in the design. Two nonlinear effects are considered in the model: the nonlinear detwinning effect of the SMA and the nonlinear geometric effect of the coil spring for large deformations. The design process is organized into six steps and is presented with a flowchart and design equations. By following this systematic approach, an SMA coil spring actuator can be designed for various applications. Experimental results verified the static two-state model for the SMA coil spring actuator and a case study showed that an actuator designed using this framework met the design requirements. The proposed design framework was developed to assist application engineers such as robotics researchers in designing SMA coil spring actuators without the need for full thermomechanical models.

Scale bridging method to characterize mechanical properties of nanoparticle/polymer nanocomposites

Multiscale analysis to characterize the size effect of silica nanoparticles on the mechanical properties of nanoparticle/polymer nanocomposites is developed and verified through a molecular dynamics simulation and continuum micromechanics model. In the micromechanics model, the particle-matrix interface mechanical property is incorporated, and the thickness and elastic properties of the interface are extracted from the atomistic structures. The proposed multiscale micromechanics model accurately reflects the size effect of the nanoparticle. The prediction by the current multiscale model at various volume fractions is compared to the results of the molecular dynamics simulations in order to validate the present multiscale analysis model.

Efficient higher-order shell theory for laminated composites

An efficient higher-order shell theory is obtained for symmetric laminated composites. The in-plane displacement fields are obtained by superimposing a globally cubic varying displacement field on a zig-zag linearly varying one. For an orthogonal curvilinear coordinate system, equilibrium equations and boundary conditions are derived using lines of curvature coordinates. Cylindrical shell equations are obtained from the general equilibrium equations. To evaluate the present shell modeling, the analytical solution for a cylindrical bending problem is obtained. The present shell theory gives deformation and stresses which are in good agreement with those of exact elasticity solutions.

The origins and mechanism of phase transformation in bulk Li2MnO3: first-principles calculations and experimental studies

Lithium-rich oxide materials are promising candidates for high-energy lithium ion batteries, but currently have critical challenges of poor cycle performance and voltage drop induced by undesirable phase transformation. To resolve these problems, it is necessary to identify the origins and mechanism of phase transformation in Li2MnO3, a key component of Li-rich oxides. In this work, the phase transformation of bulk Li2MnO3 is investigated by thermodynamic and kinetic approaches based on first-principles calculations and validated by experiments. Using the calculated thermodynamic energies, the most stable structure is determined as a function of Li extraction for Li2−xMnO3: monoclinic (x = 0.0–0.75), layered-like (x = 1.0–1.25), and spinel-like (x = 1.5–2.0) structures. The phase transformation becomes kinetically possible for Li2−xMnO3 (x > 1.0). Atomic scale origins and the mechanism of phase transformation are elucidated by the thermodynamically stable and kinetically movable tetrahedral coordination of Mn4+ in the transition state. These theoretical observations are validated by ex situ X-ray photoelectron spectroscopy combined with electrochemical experiments for Li2−xMnO3 with various Li contents upon cycling. The mechanistic understanding from theoretical calculations and experimental observations is expected to provide a fundamental solution and guidelines for improving the electrochemical performance of Li-rich oxides and, by extension, the battery performance.