The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

The Effect of Boundary Conditions and Stacking Sequence on the Nonlinear Behavior of Laminated Composite Plates in Bending

This paper presents an effectively numerical approach based on quadrilateral isoperimetric element. Indeed, the Von-Karman’s large deflection theory and the first-order shear deformation theory (FSDT) are also used in the formulation of the element to formulate the geometrically nonlinearity analysis. The nonlinear finite element code has been developed by using Matlab. Therefore, the governing nonlinear equations obtained are solved using Newton–Raphson iterative technique. Finally, the results obtained are compared with those available in the literature and with those obtained by ABAQUS. It has been found that the present approach is accurate and efficient to predict the nonlinear behavior of laminated composite plates under bending loads. Moreover, the effects of the boundary conditions and the stacking sequence on the nonlinear deflection of the plate are treated.

Cell Wall Fracture Mechanism in Ultrasonic Assisted Cutting of Honeycomb Materials

Revealing the ultrasonic cutting mechanism of honeycomb composite is important for determining the acoustic parameters of the ultrasonic system and selecting the parameters of the cutting process. Understanding more details of the stress on the cell wall from ultrasonic vibrating tool and the conditions for cell wall breakage is essential to study the machining mechanism. According to the evolution of contact state between the straight edge cutter and the honeycomb cell wall in a cycle, the cutting force acting on the cell wall is divided into three stages: transverse cutting load action, longitudinal cutting load action, and no cutting load action. The cell wall deflection and stress equations under transverse cutting load were established by applying elastic thin plate small deflection theory. The deformation and fracture characteristics of the honeycomb cell wall were analyzed by combining the analytical and the finite element model. The results showed that the ultrasonic vibration of the cutter greatly improved the stiffening effect of the cell wall and its fracture was caused by the deflection under the transverse cutting load, which exceeded the maximum allowable deformation after local stiffening. In addition, with only longitudinal cutting load, it was difficult to break the critical buckling state that leads to cell wall fracture.

The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of < 0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

Behavioural Study of Thin Plate Under Large Deflection Theory

For a thin plate, if the deformation is on the order of the thickness and stay elastic, linear theory might not turn out correct results because it does not predict the in plane movement of the member. Therefore, to account for the inconsistencies of geometric nonlinearity, large deflection theory is required [1]. This report pertains to the analytical study dispensed to check the behavior of thin plate under fixed and pinned edge conditions, and for diverse thicknesses, under the small and large deflection theories. The deformation is additionally studied, supported by Von-Karman equations. Non linear analysis has been performed on FE model using the ANSYS software. The consequences of geometric nonlinearities are mentioned. Outline on conclusion of the theoretical and experimental results obtained, are compared so as to review the similarity of the modeling and theory.

A Method to Estimate Dynamic Buckling Response of an Unstiffened Plate Elastically Restrained Along all Edges Under In-Plane Impact

Unstiffened plates in structures are usually welded or fastened to supporting members, providing rotational restraint stiffness to the plate. Previous studies have shown that neglect of rotational restraint stiffness at the edges of a plate in a structure can introduce deviations in the analysis of dynamic elastic buckling. In this study, the in-plane impact-induced dynamic elastic buckling responses of isotropic imperfect unstiffened plates with four elastically restrained edges are analytically investigated, based on the large-deflection theory of thin plate. The evolution of the peak deflection predicted by the proposed analytical method is found to be consistent with the responses available from the literature. Then the method is further used to estimate the deformation map of an unstiffened plate with four elastically restrained edges, and the effects of rotational restraint stiffness, initial geometric imperfection and shock duration on the dynamic buckling response of the plate are examined. The results show that the critical dynamic buckling load and the maximum deflection response of the plates are significantly influenced by the rotational restraint stiffness as well as the first-order initial geometric imperfection, and thus cannot be neglected in the analysis of dynamic buckling.

Geometric Non-Linear Analysis of Auxetic Hybrid Laminated Beams Containing CNT Reinforced Composite Materials

In the current work, a novel hybrid laminate with negative Poisson’s ratio (NPR) is developed by considering auxetic laminate which is composed of carbon nanotube-reinforced composite (CNTRC) and fiber-reinforced composite (FRC) materials. The maximum magnitude of out-of-plane NPR is identified in the case of (20 F/20 C/−20 C/20 C) S laminate as well. Meanwhile, a method for the geometric non-linear analysis of hybrid laminated beam with NPR including the non-linear bending, free, and forced vibrations is proposed. The beam deformation is modeled by combining higher-order shear-deformation theory (HSDT) and large deflection theory. Based on a two-step perturbation approach, the asymptotic solutions of the governing equations are obtained to capture the linear and non-linear frequencies and load-deflection curves. Moreover, a two-step perturbation methodology in conjunction with fourth-order Runge–Kutta method is employed to solve the forced-vibration problem. Several key factors, such as CNT distribution, variations in the elastic foundation, and thermal stress, are considered in the exhaustive analysis. Theoretical results for some particular cases are given to examine the geometric non-linearity behavior of hybrid beam with NPR as well as positive Poisson’s ratio (PPR).

Modeling and Experimentation of the Unidirectional Orthodontic Force of Second Sequential Loop Orthodontic Archwire

The abnormal tooth arrangement is one of the most common clinical features of malocclusion which is mainly caused by the tooth root compression malformation. The second sequential loop is mostly used for the adjusting of the abnormal tooth arrangement. Now, the shape devise of orthodontic archwire depends completely on the doctor’s experience and patients’ feedback, this practice is time-consuming, and the treatment effect is unstable. The orthodontic-force of the different parameters of the second sequence loop, including different cross-sectional parameters, material parameters, and characteristic parameters, was compared and simulated for the abnormal condition of root compression deformity. In this paper, the analysis and experimental study on the unidirectional orthodontic-force were carried out. The different parameters of the second sequential loop are analyzed, and the equivalent beam deflection theory is used to analyze the relationship between orthodontic-force and archwire parameters. Based on the structural analysis of the second sequential loop, the device for measuring orthodontic force has been designed. The orthodontic force with different structural characteristics of archwire was compared and was measured. Finally, the correction factor was developed in the unidirectional orthodontic-force forecasting model to eliminate the influence of inherent error. The average relative error rate of the theoretical results of the unidirectional orthodontic-force forecasting model is between 12.6% and 8.75%, which verifies the accuracy of the prediction model.