Improved Strategy of Two-Node Curved Beam Element Based on the Same Beam’s Nodes Information

The curved beam with a great initial curvature is the typical structure and applied widely in real engineering structures. The common practice in the current literature employs two-node straight beam elements as the elementary members for stress and displacement analysis, which needs a large number of divisions to fit the curved beam shape well and increases computational time greatly. In this paper, we develop an improved accurate two-node curved beam element (IC2) in 3D problems, combining the curved Timoshenko beam theory and the curvature information calculated from the same beam curve. The strategy of calculating the curvature information from the same bean curve in the IC2 beam element and then transferring the curvature information to the two-node straight beam element can greatly enhance the accuracy of the mechanical analysis with no extra calculation burden. We then introduce the finite element implementation of the IC2 beam element and verify by the complex curved beam analysis. By comparison with simulation results from the straight two-node beam element in the MIDAS (S2-MIDAS) and the three-node curved beam element adopted in the ANSYS (C3-ANSYS), the simulation results of the typical quarter arc examples under constant or variable curvature show that the IC2 beam element based on curved beam theory is a combination of efficiency and accuracy. And, it is a good choice for analysis of complex engineering rod structure with large initial curvature.

A Curve-Shaped Beam Bistable Piezoelectric Energy Harvester with Variable Potential Well: Modeling and Numerical Simulation

To improve the energy harvesting performance of an energy harvester, a novel bistable piezoelectric energy harvester with variable potential well (BPEH-V) is proposed by introducing a spring to the external magnet from a curve-shaped beam bistable harvester (CBH-C). First, finite element simulation was performed in COMSOL software to validate that the curved beam configuration was superior to the straight beam in power generation performance, which benefits energy harvesting. Moreover, the nonlinear magnetic model was obtained by using the magnetic dipoles method, and the nonlinear restoring force model of the curve-shaped beam was acquired based on fitting the experimental data. The corresponding coupled governing equations were derived by using generalized Hamilton’s principle, the dynamic responses were obtained by solving the coupling equations with the ode45 method. Finally, the numerical simulations showed that the proposed harvester can make interwell oscillations easier due to the spring being efficiently introduced to pull down the potential barrier compared with the conventional bistable harvester. Spring stiffness has a great impact on characteristics of the system, and a suitable stiffness contributes to realize large-amplitude interwell oscillations over a wide range of excitation, especially in the low excitation condition.

Mixed finite element formulation for bending of laminated beams using the refined zigzag theory

This study presents a mixed finite element formulation for the stress analysis of laminated composite beams based on the refined zigzag theory. The Hellinger–Reissner variational principle is employed to obtain the first variation of the functional that is expressed in terms of displacements and stress resultants. Due to C0 continuity requirements of the formulation, linear shape functions are adopted to discretize the straight beam domain with two-noded finite elements. The proposed formulation is shear locking free from nature since it introduces displacement and stress resultant terms as independent field variables. A monolithic solution of the global finite element equations is preferred, hence the stress resultants are directly obtained from the solution of these equations. The in-plane strain measures of the beam are obtained directly at the nodes over the compliance matrix and stress resultants by avoiding error-prone spatial derivatives. Following, transverse shear stresses are calculated from the equilibrium equations at the post-processing level. This simple but effective finite element formulation is first verified and tested for convergence behavior. The robustness of the approach is shown through some examples and its accuracy in predicting the displacement and stress components is revealed.

Design of Shape Reconfigurable, Highly Stretchable Honeycomb Lattice With Tunable Poisson’s Ratio

The mechanical behaviors of lattice structures can be tuned by arranging or adjusting their geometric parameters. Once fabricated, the lattice’s mechanical behavior is generally fixed and cannot adapt to environmental change. In this paper, we developed a shape reconfigurable, highly stretchable lattice structure with tunable Poisson’s ratio. The lattice is built based on a hexagonal honeycomb structure. By replacing the straight beam with curled microstructure, the stretchability of the lattice is significantly improved. The Poisson’s ratio is adjusted using a geometric angle. The lattice is 3D printed using a shape memory polymer. Using its shape memory effect, the lattice demonstrates tunable shape reconfigurability as the ambient temperature changes. To capture its high stretchability, tunable Poisson’s ratio and shape reconfigurability, a phase evolution model for lattice structure is used. In the theoretical model, the effects of temperature on the material’s nonlinearity and geometric nonlinearity due to the lattice structure are assumed to be decoupled. The theoretical shape change agrees well with the Finite element results, while the theoretical model significantly reduces the computational cost. Numerical results show that the geometrical parameters and the ambient temperature can be manipulated to transform the lattice into target shapes with varying Poisson’s ratios. This work provides a design method for the 3D printed lattice structures and has potential applications in flexible electronics, soft robotics, and biomedicine.

Experimental studies of vibrations of flexible structures induced by axial pipe flow

This thesis presents experimental studies of vibration of a straight beam and a thin plate in axial pipe flow. Dynamic behaviors of the two structures are investigated for a wide range of mean flow velocities. Responses of the structures were measured and analyzed in the time and frequency domains with an aim to understand the fluid-solid interactions. The experimental results reveal that high mean flow velocities can excite higher vibration modes because of turbulence.

Experimental studies of vibrations of flexible structures induced by axial pipe flow

This thesis presents experimental studies of vibration of a straight beam and a thin plate in axial pipe flow. Dynamic behaviors of the two structures are investigated for a wide range of mean flow velocities. Responses of the structures were measured and analyzed in the time and frequency domains with an aim to understand the fluid-solid interactions. The experimental results reveal that high mean flow velocities can excite higher vibration modes because of turbulence.

A Multi-Mode Broadband Vibration Energy Harvester Composed of Symmetrically Distributed U-Shaped Cantilever Beams

Using the piezoelectric effect to harvest energy from surrounding vibrations is a promising alternative solution for powering small electronic devices such as wireless sensors and portable devices. A conventional piezoelectric energy harvester (PEH) can only efficiently collect energy within a small range around the resonance frequency. To realize broadband vibration energy harvesting, the idea of multiple-degrees-of-freedom (DOF) PEH to realize multiple resonant frequencies within a certain range has been recently proposed and some preliminary research has validated its feasibility. Therefore, this paper proposed a multi-DOF wideband PEH based on the frequency interval shortening mechanism to realize five resonance frequencies close enough to each other. The PEH consists of five tip masses, two U-shaped cantilever beams and a straight beam, and tuning of the resonance frequencies is realized by specific parameter design. The electrical characteristics of the PEH are analyzed by simulation and experiment, validating that the PEH can effectively expand the operating bandwidth and collect vibration energy in the low frequency. Experimental results show that the PEH has five low-frequency resonant frequencies, which are 13, 15, 18, 21 and 24 Hz; under the action of 0.5 g acceleration, the maximum output power is 52.2, 49.4, 61.3, 39.2 and 32.1 μW, respectively. In view of the difference between the simulation and the experimental results, this paper conducted an error analysis and revealed that the material parameters and parasitic capacitance are important factors that affect the simulation results. Based on the analysis, the simulation is improved for better agreement with experiments.

Analysis of the effect of the secondary moment on curved beams of full cross section

abstract This paper analysis the effect of the secondary moment on curved beams using the equivalent nodal loads method. A case study was carried out applying the equivalent nodal loads method to a two-span prestressed curved beam, using a curved finite element as the structural model, analyzing the effect of the secondary moment for each case and comparing it with its equivalent in straight beam. It was found that the stiffness parameters E I and G J influence the secondary moment. The results demonstrates that the beam opening angle reduces the effect of secondary moment, and that the greater the angle, the greater is the reduction that occurs in its secondary moment compared to its equivalent straight beam.