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.

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.

Capacitance Response of Concave Well Substrate MEMS Double Touch Mode Capacitive Pressure Sensor: Robust Design, Theoretical Modeling, Numerical Simulation and Performance Comparison

Touch Mode Capacitive Pressure Sensor (TMCPS) is very suitable for industrial applications where pressure sensing is necessary because of their linearity, mechanical robust nature and large overload protection from harsh industrial condition. This work proposes an introduction of a notch in the concave substrate for further improvement of the sensitivity of the sensor. Small deflection mode is utilized for the mathematical analysis of the design proposed and MATLAB is utilized for all the software simulations. The sensitivity of the proposed model is very high compared to other models with flat substrate. The analysis and simulation show significant increase in sensitivity in touch mode. The pressure at which the value of the capacitance saturates is also much higher than the designs stated in the literature. The analysis of concave substrate Double Touch Mode Capacitive Pressure Sensor (DTMCPS) will be helpful in designing new sensor for performance increase and to evaluate the behaviour of it.

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.

Design and simulation of piezoelectric nano cylindrical hollow structure for energy harnessing applications

This article investigates piezoelectric materials for harnessing vibrational energy. A nano hollow cylindrical structure based on various piezoelectric materials was designed and utilised to generate the voltage. An accurate and efficient model is developed here, so as to optimized the efficiency of the piezoelectric energy harvester. This work analyses the piezoelectric actuator deflection and involves the Eigen frequency computation. A measurement methodology for investigating the mechanical and electrical behaviour of vibrational harvester's was modelled and analysed by finite element method using COMSOL software. The energy harvesting structure was developed and tested with different piezoelectric materials to attain appreciable voltage through a small deflection. The Simulated results predicts that for the same pressure range, different piezoelectric materials have the different output voltage and Eigen frequencies. The maximum voltage was observed for Barium Titanate (3.0847 V at 250 µm), along with poled Polyvinylidene fluoride. In addition, a comparison was made with different piezoelectric materials ideally suited to intelligent cantilever structure. For optimizing the performance of the piezoelectric energy harvester an accurate and efficient model is required, which was developed in this simulation study. A high voltage value with a small deflection through a cylindrical hollow structure was designed and tested using various piezoelectric materials in this study.

A Concise and Geometrically Exact Planar Beam Model for Arbitrarily Large Elastic Deformation Dynamics

The potential of large elastic deformations in control applications, e.g., robotic manipulation, is not yet fully exploited, especially in dynamic contexts. Mainly because essential geometrically exact continuum models are necessary to express these arbitrarily large deformation dynamics, they typically result in a set of nonlinear, coupled, partial differential equations that are unsuited for control applications. Due to this lack of appropriate models, current approaches that try to exploit elastic properties are limited to either small deflection assumptions or quasistatic considerations only. To promote further exploration of this exciting research field of large elastic deflection control, we propose a geometrically exact, but yet concise a beam model for a planar, shear-, and torsion-free case without elongation. The model is derived by reducing the general geometrically exact the 3D Simo–Reissner beam model to this special case, where the assumption of inextensibility allows expressing the couple of planar Cartesian parameters in terms of the curve tangent angle of the beam center line alone. We further elaborate on how the necessary coupling between position-related boundary conditions (i.e., clamped and hinged ends) and the tangent angle parametrization of the beam model can be incorporated in a finite element method formulation and verify all derived expressions by comparison to analytic initial value solutions and an energy analysis of a dynamic simulation result. The presented beam model opens the possibility of designing online feedback control structures for accessing the full potential that elasticity in planar beam dynamics has to offer.

The experimental investigation of the failure of load-bearing masonry walls supported by a deflecting structure

The paper presents selected results of tests of full-scale masonry walls linearly supported on a deflecting beam. The walls with thin bed joints and unfilled head joints were 4.55 m long and 2.45 m high, and were made of group 1 calcium silicate masonry units. The tests included walls with and without openings. The tests were carried out in a specially designated and constructed test stand, which allowed simultaneous vertical load on the upper edge of the wall and vertical deflection of the beam supporting this wall. During the test, measurements of mutual displacements of six points on the wall surface were carried out. On both faces of masonry specimens, the changes of the length of the measuring bases connecting these six points were recorded. Walls without openings were detached from the central part of the supporting beam at a deflection not exceeding 2 mm. Walls with one door opening also cracked at an early stage of tests. In this case, a detachment from the supporting beam and cracking at the ends of the lintel occurred because of the rotation of the pillars connected by the lintel above the opening. In walls with two door openings, first cracks were formed at the ends of lintels due to the rotation of pillars with a small deflection of the supporting beam, less than 3 mm. Whereas, in walls with door and window openings, first cracks occurred under the window and at the end of the lintel in the outer pillar of the wall.