Quasi-static Numerical Simulations Research Articles

Quasi-Static Numerical Simulations and Resilient Force Models of GFRP-Confined FRP Bar-Reinforced Concrete Piers

Quasi-Static Numerical Simulations and Resilient Force Models of GFRP-Confined FRP Bar-Reinforced Concrete Piers

Finite deformation micropolar peridynamic theory: Variational consistency of wryness measure

This paper concerns developments in both classical and peridynamic (PD) finite deformation micropolar elasticity theory. The first part presents an alternative proof of a theorem that demonstrates variational consistency of the wryness measure in classical finite deformation micropolar elasticity which is one of the novel contributions of this work. The linearized version of the proposed wryness measure is compared with the wryness measure of small deformation micropolar elasticity. In the second part of this work, a finite deformation micropolar PD theory is presented. After proposing an additional integro-differential equation along with the standard PD equation of motion, the global balance of angular momentum is proved to be satisfied. The balance of virtual work is derived for the micropolar PD theory. Next, constitutive correspondence approach is used to relate PD force and moment states with their classical counterparts. The nonlocal versions of the strain and the proposed wryness measure are used in the constitutive correspondence. The constitutive equations of the classical micropolar theory are presented and how they can be incorporated in PD framework is discussed. We introduce a new bond breaking criterion for PD micropolar materials based on critical stretch and critical relative rotation. Quasi-static numerical simulations on deformations of plate with a hole and fracture of a double notched sheet are presented. Dynamic simulations concern wave propagation through a solid specimen and plate with a hole. Validation of the simulation results with the finite element solutions, boundary element solutions, and experimental observations demonstrate the potential of our approach.

High-speed plasma measurements with a plasma impedance probe

Plasma impedance probes (PIPs) are a type of RF probe that primarily measures electron density. This work introduces two advancements: a streamlined analytical model for interpreting PIP-monopole measurements and techniques for achieving ≥1 MHz time-resolved PIP measurements. The model’s improvements include introducing sheath thickness as a measurement and providing a more accurate method for measuring electron density and damping. The model is validated by a quasi-static numerical simulation, which compares the simulation with measurements, identifies sources of error, and provides probe design criteria for minimizing uncertainty. The improved time resolution is achieved by introducing higher-frequency hardware, updated analysis algorithms, and a more rigorous approach to RF calibration. Finally, the new model and high-speed techniques are applied to two datasets: a 4 kHz plasma density oscillation resolved at 100 kHz with densities ranging between 2 × 1014 and 3 × 1015 m−3, and a 150 kHz oscillation resolved at 4 MHz with densities ranging between 4 × 1014 and 6 × 1014 m−3.

Quasi-static numerical simulation of the dynamic launching process for high-altitude balloon

In this paper, by establishing a set of mathematical models and computing methods, the numerical simulation of the ground dynamic launching process under the quasi-static assumption for a high-altitude balloon system is conducted to reveal the rich mechanical and geometric behaviors involved in it. The mathematical model includes the solution of the bubble shapes and the kinematic analysis, as well as the static model of the “membrane bundle system”. Considering the middle and lower region of the bubble still meet the zero circumferential stress condition under the hydrostatic pressure gradient, the upper fully expanded shape generatrix is the same as the balloon generatrix of the ceiling height. The multiple shooting method combined with Sequential Quadratic Programming (SQP) is used to solve the lower partially expanded bubble generatrix. Based on the force balance equations of the microelement in “membrane bundle system”, and considering the friction force in contact with the horizontal ground and the characteristics that the membrane bundle is a variable mass system along the arc length direction, the “multiple shooting method + SQP” method is still used to solve the shape and internal force of the “membrane bundle system” under two end geometric boundary conditions. In co-simulation, taking the dynamic launching process of the zero-pressure balloon system with the ceiling flight height of 30 km and hanging a load of 300 kg as the object, under the conditions of 1.5 m/s and 4.5 m/s wind speeds, the initial layout and the rising process of dynamic launching is calculated. Through the analyses of the simulation results, four stages of the rising process are concluded, namely, the stage of the “membrane bundle system” relaxation and falling to the ground, the longitudinal rising stage, the main rising stage, and the straightening stage. The geometry and force characteristics of the bubble and the “membrane bundle system” are discussed to provide a reference for the simulation of the actual high-altitude balloon ground dynamic launching testing.

Effect of metal and polymer mating gears on the bending fatigue performance of asymmetric polymer gears

The material of the mating gear influences the fatigue life of polymer gears. The bending fatigue characteristics of polyamide 66 asymmetric gears (34°/20° and 20°/34°) corresponding to steel–polymer and polymer–polymer material combinations were investigated. The performance of symmetric gear pairs (20°/20°) was determined to serve as a comparison. Quasi-static numerical simulations were performed in a finite element analysis tool to predict root bending stress, load sharing ratio, and tooth deflection. The bending fatigue strength of steel–polymer and polymer–polymer pairs of each test configuration was determined using bending fatigue tests. The load sharing ratio and root bending stress of polymer–polymer pairs decreased substantially compared to steel–polymer pairs. The extent of deflection-induced load sharing was greater in polymer–polymer pairs. The bending fatigue life of polymer–polymer pairs was lower than that of steel–polymer pairs owing to the higher operating temperature. In polymer–polymer pairs, polymer driving and driven gears increased the heat generated and diminished the heat dissipation to the environment. In steel–polymer and polymer–polymer pairs, the configuration with the highest bending fatigue strength was 34°/20° and 20°/34°, respectively. This divergence was caused by the increase in temperature difference between the two configurations for polymer–polymer pairs. Analysis of hysteresis loops indicated that the loop area was higher for polymer–polymer pairs, signifying the increased amount of dissipated energy. No noticeable variation was observed between the failure modes of steel–polymer and polymer–polymer pairs despite the significant difference in the operating temperatures. The bending stress and operating temperature were the dominant factors affecting the performance of steel–polymer and polymer–polymer gear pairs, respectively.

Upside down glass of water experiment revisited

A glass of water covered with a disk with a hole in it can be turned upside down without spilling the water in the glass, provided the hole is small enough and the disk is pressed against the rim of the glass. A quasistatic numerical simulation based on hydrostatic pressure and surface tension of water was used calculate the critical hole diameter when the water will begin to drain. The model predicts a critical hole diameter of 15.25 mm. Experimentally it was found tha a hole diameter of 15.1 mm was still small enough to keep the water from draining.

Role of multiscale heterogeneity in fault slip from quasi-static numerical simulations

Quasi-static numerical simulations of slip along a fault interface characterized by multiscale heterogeneity (fractal patch model) are carried out under the assumption that the characteristic distance in the slip-dependent frictional law is scale-dependent. We also consider slip-dependent stress accumulation on patches prior to the weakening process. When two patches of different size are superposed, the slip rate of the smaller patch is reduced when the stress is increased on the surrounding large patch. In the case of many patches over a range of scales, the slip rate on the smaller patches becomes significant in terms of both its amplitude and frequency. Peaks in slip rate are controlled by the surrounding larger patches, which may also be responsible for the segmentation of slip sequences. The use of an explicit slip-strengthening-then-weakening frictional behavior highlights that the strengthening process behind small patches weakens their interaction and reduces the peaks in slip rate, while the slip deficit continues to accumulate in the background. Therefore, it may be possible to image the progress of slip deficit at larger scales if the changes in slip activity on small patches are detectable.

Crashworthiness design for trapezoid origami crash boxes

A thin-walled tube referred to as trapezoid origami crash box is recognized as an energy absorption device. The surface of this tube is prefolded in the light of a developable origami pattern that is delicately designed to introduce a special structure on the surface of a square tube. This special structure, known as trapezoid folded lobe, is employed as a type of geometric imperfection to lower the peak force and as a mode inducer to trigger the complete diamond mode. The quasi-static numerical simulations reveal that the complete diamond mode is successfully triggered. Moreover, geometric and compliance analysis suggest that three key parameters, the number of module M, dihedral angle θ and area ratio ω, could greatly affect the collapse behavior. Based on those analysis, an optimal trapezoid origami crash box is designed to compare with the conventional square and octagonal tubes of identical weight. Furthermore, a series of diamond origami crash boxes are analyzed to compare with the trapezoid origami crash boxes. The comparative results show that the trapezoid origami crash box is the most desirable in terms of energy absorption.

On the stability of geotechnical systems and its fractal progressive loss

Geotechnical systems, consisting of soil and embedded solid structures, are practically stable if inevitable actions cause at most harmless redistributions. This kind of robustness can often be achieved with limit state design, i.e. by assuming representative snapshots of worst cases. Changes in configuration and state due to changing boundary conditions can be better judged with quasi-static numerical simulations using validated constitutive relations. The ever-present fractality of the ground may be neglected as long as the system is stable, whereas it gets dominant during a progressive loss of stability with jerky critical phenomena which elude mathematical treatment until present. In this sense geotechnical systems can be or get sensitive, i.e. further actions can trigger detrimental chain reactions with seismogeneous collapse of the soil fabric, pore pressure increase up to liquefaction, erosion, cracking of ground and structural parts and/or tilting. The geotechnical risk can be better mitigated by taking into account chain reactions with wild randomness. It can be further reduced by monitoring the seismic emission in addition to mass flows, structural deformations and pore pressures. The paper is to clarify notions and concepts.

A wear-reduced nanodrive based on oscillating rolling

In this article we introduce a promising new concept for a high precision actuator. It is based on inertia effects and oscillating rolling. A sphere acts as the drive and is pressed on a movable substrate that acts as the runner. A combination of oscillating translation and rotation of the sphere induces motion of the runner. A varying normal force leads to varying indentation depth and contact area. This asymmetry together with the inertia of the runner enables accurate control of its displacement. As slip is completely omitted here, in theory the actuator works principally wearless. We use the method of dimensionality reduction to conduct a quasistatic numerical simulation of the system. In addition we derive analytical expressions for the steady working points of the system that are in perfect agreement with the simulation results.

Modelling reinforced concrete beams under mixed shear-tension failure with different continuous FE approaches

The paper presents quasi-static numerical simulations of the behaviour of short reinforced concrete beams without shear reinforcement under mixed shear-tension failure using the FEM and four various constitutive continuum models for concrete. First, an isotropic elasto-plastic model with a Drucker-Prager criterion defined in compression and with a Rankine criterion defined in tension was used. Next, an anisotropic smeared crack and isotropic damage model were applied. Finally, an elasto-plastic-damage model was used. To ensure mesh-independent FE results, to describe strain localization in concrete and to capture a deterministic size effect, all models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. Bond-slip between concrete and reinforcement was considered. The numerical results were directly compared with the corresponding laboratory tests performed by Walraven and Lehwalter (1994). The advantages and disadvantages of enhanced models to model the reinforced concrete behaviour were outlined.

Energy Absorption of Thin-Walled Square Tubes With a Prefolded Origami Pattern—Part I: Geometry and Numerical Simulation

Thin-walled tubes subjected to axial crushing have been extensively employed as energy absorption devices in transport vehicles. Conventionally, they have a square or rectangular section, either straight or tapered. Dents are sometimes added to the surface in order to reduce the initial buckling force. This paper presents a novel thin-walled energy absorption device known as the origami crash box that is made from a thin-walled tube of square cross section whose surface is prefolded according to a developable origami pattern. The prefolded surface serves both as a type of geometric imperfection to lower the initial buckling force and as a mode inducer to trigger a collapse mode that is more efficient in terms of energy absorption. It has been found out from quasi-static numerical simulation that a new collapse mode referred to as the completed diamond mode, which features doubled traveling plastic hinge lines compared with those in conventional square tubes, can be triggered, leading to higher energy absorption and lower peak force than those of conventional ones of identical weight. A parametric study indicates that for a wide range of geometric parameters the origami crash box exhibits predictable and stable collapse behavior, with an energy absorption increase of 92.1% being achieved in the optimum case. The origami crash box can be stamped out of a thin sheet of material like conventional energy absorption devices without incurring in-plane stretching due to the developable surface of the origami pattern. The manufacturing cost is comparable to that of existing thin-walled crash boxes, but it absorbs a great deal more energy during a collision.

Dynamics of capillary self-alignment for mesoscopic foil devices

We report experimental evidence for three sequential, distinct dynamic regimes in the capillary self-alignment of centimeter-sized foil dies released at large uniaxial offsets from equilibrium. We show that the initial transient wetting regime, along with inertia and wetting properties of the dies, significantly affect the alignment dynamics including the subsequent constant acceleration and damped oscillatory regimes. An analytical force model is proposed that accounts for die wetting and matches quasi-static numerical simulations. Discrepancies with experimental data point to the need for a comprehensive dynamical model to capture the full system dynamics.

Stabilized interface methods for mechanical joints: Physics-based models and variationally consistent embedding

This paper presents the application of a new method for interfacial modeling utilizing a merger of continuous Galerkin and discontinuous Galerkin concepts to simulate the behavior of mechanical joints. The interfacial flux terms arising naturally from the discontinuous Galerkin treatment provide a mechanism to embed friction models in a variationally consistent fashion. Due to the unbiased implementation of the interface, facilitated by avoiding the master–slave concept, the deformation of the two interacting surfaces conforms to the local material and geometric attributes of the surfaces. This results in a better preservation of physics in interface mechanics. Additionally, the method is incorporated into a Variational Multiscale framework that comes equipped with a built-in error estimation module, providing numerical estimation of convergence and distinguishing discretization errors from modeling errors. A series of quasi-static numerical simulations of a lap joint under fretting conditions are conducted to compare the performance of two friction models: (i) classical Coulomb friction model and (ii) physics-based multiscale model. Hysteresis study of a three-dimensional double-bolted lap joint for the two friction models is also presented and the computed results are shown to be consistent between conforming and nonconforming meshes.

Experimental Analysis and Quasi-Static Numerical Idealization of Dynamic Stresses on a Heavy Truck Chassis Frame Assembly

The current trend in automotive design is to optimize components for weight. To achieve this, automotive designers need to have complete understanding of various stresses prevalent in different areas of the component. The chassis frame assembly of a heavy truck used for long distance goods hauling application is chosen for this investigation and dynamic stress-strain response of the component due to braking and cornering maneuvers are experimentally measured and reported. A quasi-static approach that approximates the dynamic maneuvers into number of small processes having static equilibriums is followed to carry out the numerical simulation, approximating the dynamic behavior of frame rail assembly during cornering and braking. With the help of commercial finite element package ANSYS, the quasi-static numerical simulations are carried out and compared with experimental results. This study helps in understanding prevailing stresses in truck frame rails especially during cornering and braking maneuvers and brings out all geometric locations that may be potential failure initiation locations. This study makes a case for further investigation on the effects of residual and assembly stresses on frame rails.

Efficient design analysis of a novel magnetic gear on a high performance computer

PurposeAims to show that efficiency and accuracy of integral equation methods (IEMs) in combination with the fast multipole method for the design of a novel magnetic gear.Design/methodology/approachA novel magnetic gear was developed. Magnetic fields and torque of the gear were simulated based on IEMs. The fast multipole method was applied to compress the matrix of the belonging linear system of equations. A computer cluster was used to achieve numerical results within an acceptable time. A three‐dimensional post‐processing and visualization of magnetic fields enables a deep understanding of the gear.FindingsIEMs are very well suited for the numerical analysis of a magnetic gear. Especially, the treatment of the air gap between the rotating components, which move with significant varying velocities, is relatively easy. Furthermore, a correct computation and visualization of flux lines is possible. A magnetic gear is advantageous for high rotational velocities.Research limitations/implicationsA quasi static numerical simulation has sufficed for an understanding of the principle of the magnetic gear and for the development of a prototype.Practical implicationsIEMs are very suitable for the analysis of complex problems with moving parts. Nowadays, the efficiency is very good even for large problems, since matrix compression techniques are well‐engineered.Originality/valueThe design of a novel magnetic gear is discussed. Well‐known techniques like IEMs, fast multipole method and parallel computing are combined to solve a very large and complex problem.