Minimum Stiffness Research Articles

Determination of strut-and-tie models for structural concrete under dynamic loads

This proposed study aims to develop reliable and efficient numerical optimization methods for generating optimal strut-and-tie models (STMs) in structural concrete members under dynamic loads. The numerical models are developed based on the bidirectional evolutionary structural optimization (BESO) method for the stiffness maximization problems. In this method, a controlling index based on the minimum weight and maximum stiffness is defined as the optimization criterion function and the element virtual strain energy is taken as the element removal and addition criterion. By the dynamical analysis, optimal strut-and-tie models are established based on the BESO method. Several examples are presented to show the efficiency of the proposed approach in finding optimal STMs under dynamic loads. It is shown that optimal STMs and reinforcement layouts under dynamic loads generally differ from those obtained under static loads. The developed numerical models based on dynamic responses can be used by practicing design engineers for the analysis and design of STMs in concrete structures.

Use of viscoelastic links for seismic pounding mitigation under random input

Purpose The purpose of this paper is to study the effects of viscoelastic links between two adjacent buildings for pounding mitigation under white-noise seismic input. Design/methodology/approach A formulation is first extracted for the effective modal damping ratios of the system. Then, two single DOF linear buildings connected by viscoelastic links are considered with both classical and non-classical damping schemes. The inelastic behavior is also taken into account by using equivalent natural frequencies and damping ratios of the buildings. The effect of ground dominant frequency and damping on the displacement response is also investigated by using Kanai‒Tajimi filtered white noise as the random input. Findings The difference between classical and non-classical damping is shown to be less than 20 percent, implying the permission in using the simpler classical damping scheme. Finally, the problem is extended to two-storey buildings, where using viscoelastic links only at the top story level of the buildings is shown to be sufficient for controlling individual, as well as relative, motions of the structures. Originality/value Results demonstrate that the use of link with a moderate stiffness may reduce the stiffer building displacement up to approximately 20 percent in comparison to the free displacement, while the seismic pounding of the adjacent buildings is effectively controlled. Further, an upper limit of link stiffness is obtained for preventing the increase in the stiffer building displacement, which may be exceeded by the minimum link stiffness necessary for pounding prevention if small gap size exists.

Research on structural optimization of 3-TPT parallel mechanism based on stiffness characteristics

Aiming at the problem of weak stiffness of parallel mechanism, the structural dimension was optimized according to the main influencing factors under the condition of static equilibrium. The influence of each component on the stiffness of the branched chain was analyzed by solving the stiffness of the branched chain. The stiffness matrix of whole machine was obtained by using analytical model method, which was analyzed and simulated by means of minimum eigenvalue method and static stiffness performance quotient. The optimal mathematical model was established by improving the minimum eigenvalue of limit points on the boundary as the optimization objective, the working space as the constraint condition, and the size of the main structure as the design variable. Then the size optimization of the 3-TPT parallel mechanism was conducted to improve the stiffness in the workspace. The validity of improved stiffness is verified by the minimum eigenvalue method and the static stiffness performance evaluation method.

Impact of design parameters on working stability of the electrothermal V-shaped actuator

This paper mentions a detail calculation of the equivalent dynamic parameters in differential equations of motion of the electrothermal V-shaped actuator. A heat transfer model for a thin beam (including the dependence of material properties on the temperature) is applied in order to solve more exactly temperature distribution and displacement of V-shaped beam system. Comparing the values of displacement in both calculation and simulation confirmed a higher accuracy of proposed equations. Moreover, a related formula between the minimum conversion stiffness and driving voltage amplitude is analyzed and examined to avoid the buckling phenomenon may occur in V-shaped beam system while working at a high voltage.

Numerical and experimental investigation of the full-scale buckling-restrained steel plate shear wall with inclined slots

Abstract This paper presents a buckling-restrained steel plate shear wall with inclined slots (simply referred as “slotted SPSW”) with own boundary columns, which can be used as a novel lateral force resistant system. The slotted SPSW is only connected with the structural beam, which reduces the effect on the structural column, avoiding premature failure of the structural column. Therefore, numerical analyses are used to investigate the interaction between the boundary column and the slotted SPSW. The formula of the minimum flexural boundary column stiffness is provided. Some key parameters, such as the steel plate aspect ratio, slenderness, and the width of inclined slots, are studied through parametric analysis. Numerical analyses results show that the axial force, shear force and bending moment increase with the steel plate aspect ratio, and decrease with the increasing of steel plate slenderness and the inclined slot width. Then theoretical calculation method of internal force in the boundary column is provided. Finally, in order to understand the seismic behavior of the slotted SPSW with boundary column under quasi-static cyclic loading, one full-scale test specimen is designed and tested. When boundary column is properly designed, the slotted SPSW with boundary column has a ductile behavior and stable energy dissipation capacity.

Direct laser writing to fabricate capacitively transduced resonating sensor

This article reports on laser technology based fabrication approach to develop a micro-size capacitive gap based transducer useful for a variety of applications. A low-cost prototype has been fabricated via a rapid and advanced laser micro-milling technique to achieve a parallel kerf-width (capacitive gaps) of about 60 µm into a piece of aluminum and a stainless steel each of 1 and 2 mm thickness, respectively, thus leading to a high-aspect ratio (> 33) structure. A device is demonstrated to facilitate actuation via electrostatic means and sense a capacitive change across its electrode. Experiments have been performed with a structure made of aluminum. Results comprising analytical modeling, fabrication, and electrical characterization are presented. An applicability of a device as a two degree-of-freedom resonating mode-localization sensor that employs a weak electrostatic coupling is demonstrated to offer vibration amplitude based sensitivity to a relative change in the stiffness. This sensor is able to resolve a minimum stiffness perturbation (normalized), $$\delta_{{k_{\rm{min} } }} = \frac{\Delta k}{{K_{eff} }}$$ of the order of 7.98 × 10−4.

Optimization of Drillstring Design to Produce More Stable Dynamic Drilling on Horizontal Drilling by Applying Different Stiffness Combinations

Horizontal drilling technique is one of the methodologies that have been widely implemented recently to improve the production of oil and gas wells. Several directional drilling technologies can be utilized to drill the horizontal wells, vary from the simple mud motor technology to Bottom Hole Assembly (BHA) with the advanced motorized rotary steerable system. The most common challenges that are faced on horizontal drilling process are on the torque and the stick-slip throughout drilling process, which can be a technical limiter for the length of horizontal section that would be achieved. Stick-slip is the vibration that occurs due to cyclical rotation acceleration and deceleration of the bit, BHA or drill string. This speed fluctuation can be zero to rate of penetration (ROP) or far in excess of twice the rotational speed measured at the surface. Stick-slip can significantly decrease the ROP, increases tool failures and damage, affects borehole quality, and impacts the data acquisition. Several studies had been done on the stick-slip prevention and mitigation throughout creation of new technology and drilling parameters envelope throughout drilling operation, however no study has ever been done on the modification of the design and arrangement of the BHA itself to produce more stable BHA. Drill pipe is the longest component of the drill string and hence it has biggest contribution towards the drill string dynamic. This study will focus on the analysis of the combination of several designs of the drill-pipe and heavy weight drill-pipe (HWDP) that has different stiffness and characteristic to produce less vibration, more efficient drilling operation and to create zero impact on the data acquisition measured while drilling. FEA drilling dynamic simulator was used to optimize the drill sting configuration. The calculation is made from the depth of 750 m to 2801 m. Based on the drilling simulation results of FEA modeling, it is concluded that the minimum stiffness ratio to give stability of the drill string of Well-Z7 BHA and Well-Z6 BHA is 0.012175272 and 0.07366999, respectively.

Spatially resolved acoustic spectroscopy for integrity assessment in wire–arc additive manufacturing

Wire–arc additive manufacturing (WAAM) is an emergent method for the production and repair of high value components. Introduction of plastic strain by inter-pass rolling has been shown to produce grain refinement and improve mechanical properties, however suitable quality control techniques are required to demonstrate the refinement non-destructively. This work proposes a method for rapid microstructural assessment of Ti–6Al–4V, with limited intervention, by measuring an acoustic wave generated on the surface of the specimens. Specifically, undeformed and rolled specimens have been analysed by spatially resolved acoustic spectroscopy (SRAS), allowing the efficacy of the rolling process to be observed in velocity maps. The work has three primary outcomes (i) differentiation of texture due to rolling force, (ii) understanding the acoustic wave velocity response in the textured material including the underlying crystallography, (iii) extraction of an additional build metric such as layer height from acoustic maps and further useful material information such as minimum stiffness direction. Variations in acoustic response due to grain refinement and crystallographic orientation have been explored. It has been found that the limited α-variants which develop within prior-β grains lead to distinctive acoustic slowness surfaces. This allowed prior-β grains to be resolved. A basic algorithm has been proposed for the automated measurement, which could be used for in-line closed loop control. The practicality and challenges of applying this approach in-line with fabrication are also discussed.

Multi-objective optimization of parallel manipulators using a game algorithm

• A multi-objective optimization method using game algorithm for parallel manipulators is proposed. • A new stiffness index considering the coupling effect of the non-diagonal elements is proposed. • A new index which defines the difference between the total and principal diagonal stiffness indices is proposed. • A four-dimensional intuitive image of slice distribution of the index is presented. In this paper, a multi-objective optimization game algorithm (MOOGA) for parallel manipulators (PMs) is proposed. The proposed algorithm considers the volume of the regular cylindrical workspace, motion/force transmission performance, and stiffness performance as objective functions. First, the distributions of the objective functions in the complete parameter space are calculated and sorted by importance. Second, game weighting factors and lower bound values are assigned to different objective functions according to the engineering requirements. Finally, after multiple rounds of gaming according to the weighting factors and lower bound values, the objective functions reach an optimal balance point and obtain a balance intersection subspace. In addition, a new comprehensive stiffness index (CSI) is proposed, that takes the coupling of the non-diagonal elements into consideration. This index decouples the linear and angular stiffness and has definite physical dimensions as well as a clear physical meaning. A Lagrangian function is used to obtain the maximum and minimum stiffnesses at a given position along with their corresponding directions. To compare the difference between the CSI and the principal diagonal stiffness index (PDSI), a divergence index κ is proposed. 2UPR–RPU and 2UPR–2RPU PMs are employed as examples to implement the proposed algorithm, where U, P and R denote a universal joint, prismatic pair and revolute pair, respectively. The corresponding slice distributions of the local CSI and κ in the regular cylindrical workspace are presented. Additionally, the distributions of the extreme linear stiffness indices and their corresponding directions are presented. The results show that the CSI is decreased by 99% relative to the PDSI. The numerical results demonstrate the effectiveness of the algorithm proposed in this paper.

Minimum foundation size and spacing for jacket supported offshore wind turbines considering dynamic design criteria

Modes of vibration play a dominant role in the design of WTG (Wind Turbine Generator) support structures. It is necessary to choose the overall system frequency such that the modes of vibration do not coincide with the rotor frequencies as well as the wave frequencies. WTG supported on multiple foundations (such as jackets or seabed frames) may exhibit rocking modes of vibration if the vertical stiffness of the foundation is not large enough which in turn may have serious implications on the fatigue performance of the overall structure. From the O&M (Operation and Maintenance) point of view, it is necessary to design the overall system to have sway-bending as the dominant mode of vibration. This paper develops a formulation for obtaining foundation (for both piles and shallow suction caissons) sizes and spacing such that rocking vibrations are prevented and sway-bending vibrations are achieved. Expressions for the minimum vertical stiffness of foundations are proposed for different configurations: square base, symmetrical (equilateral) triangle, or asymmetrical (isosceles) triangle. Verification of the method is carried out through finite element analysis and a step-by-step solved example is taken to show the application of the formulation. It is hoped that the formulation will assist designers to optimize the foundation arrangement and provide preliminary sizing for tender design.

Design of Transverse Stiffeners in Plate Girders with Corrugated Web

This study reports investigations into the effect of relative flexural stiffness of intermediate stiffeners γ on the failure zone location in the corrugated web. The study also aimed at obtaining stiffness criterion for intermediate stiffeners that depends on the magnitude of the plate geometry parameter α. To achieve the goals of the study, experimental investigations were conducted into load displacement paths of four exemplary SIN girders. They were simply supported girders, made to full scale, and composed of pre-assembled units. The phenomena occurring in the experiment were represented using the Finite Element Method. For FEM numerical analysis of girders with intermediate stiffeners, models with the web height of 1000, 1250 and 1500 mm, made from 2; 2.5 and 3 mm thick corrugated sheet metal were used. Due to the analysis of 52 girder numerical models, it was possible to propose the stiffness criterion of intermediate stiffeners. The criterion was based on the assessment of shear buckling strength of the corrugated web. Using the regression method, dimensionless coefficients of the stiffener stiffness ks dependent on the optimum stiffness γ were determined. Based on estimated coefficients of the stiffener stiffness ks, the absolute minimum stiffness of intermediate stiffeners Ismin used in corrugated web plate girders was calculated. It was demonstrated that the use of an intermediate stiffener, the stiffness of which is greater than Ismin , additionally leads to a change in the location of the site of the web shear buckling.

Second-order analysis of a beam-column on elastic foundation partially restrained axially with initial deflections and semirigid connections

The second-order analysis of a prismatic beam-column on elastic foundation with initial transverse deflections and semi-rigid end-connections subject to transverse load is presented. The simultaneous effects of bending and shear deformations, and concentric axial forces at both ends are also included. The transverse loads and the initial deflections are expressed using Fourier series allowing the modeling of any type of applied loads and initial imperfections. The proposed structural method is also capable of capturing the phenomenon of snap-through, snap-back (i.e, buckling reversals) as well as the values of the beam elastic critical loads and corresponding buckling shapes and the post-buckling behavior. Three comprehensive examples are presented in detail that shows the accuracy and simplicity of the proposed method. From this study it is concluded that: 1) unconnected deflection trajectories are separated by the critical loads; 2) there is a minimum stiffness of the elastic horizontal spring located at one of the ends of the beam-column that guarantees its lateral stability; and 3). there is also a minimum value for the geometric parameter m that guarantees the beam-column lateral stability.

A simple method for determining ligament stiffness during total knee arthroplasty in vivo

A key requirement in both native knee joints and total knee arthroplasty is a stable capsular ligament complex. However, knee stability is highly individual and ranges from clinically loose to tight. So far, hardly any in vivo data on the intrinsic mechanical of the knee are available. This study investigated if stiffness of the native ligament complex may be determined in vivo using a standard knee balancer. Measurements were obtained with a commercially available knee balancer, which was initially calibrated in vitro. 5 patients underwent reconstruction of the force-displacement curves of the ligament complex. Stiffness of the medial and lateral compartments were calculated to measure the stability of the capsular ligament complex. All force-displacement curves consisted of a non-linear section at the beginning and of a linear section from about 80 N onwards. The medial compartment showed values of 28.4 ± 1.2 N/mm for minimum stiffness and of 39.9 ± 1.1 N/mm for maximum stiffness; the respective values for the lateral compartment were 19.9 ± 0.9 N/mm and 46.6 ± 0.8 N/mm. A commercially available knee balancer may be calibrated for measuring stiffness of knee ligament complex in vivo, which may contribute to a better understanding of the intrinsic mechanical behaviour of knee joints.

Direct estimation of the P-delta effect through the “stability-coefficient-response-spectra” by introducing the “first-storey-single-degree-of-freedom” system

Present study introduces two concepts for direct estimation of P-delta effect in both, strength based, and displacement based design methods. Although various previously conducted studies focused on inclusion of P-delta effect into the aforementioned design methods, development of reliable procedures is still attractive. The major argument of present study is that: treatment of P-delta effect can be enhanced by using an alternative response/design spectrum. To this end, and based on period-dependence feature of stability coefficient (SC), the “stability coefficient response spectra” (SCRS) is introduced. The SCRS, plots spectral acceleration versus SC, instead of period, for a pendulum with known height. To facilitate implementation of SCRS on multi-degree-of-freedom systems, and by considering some special features of the first-storey, the concept of “first-storey-single-degree-of-freedom” (FSSDOF) system is introduced. The FSSDOF system permits setting the minimum necessary lateral stiffness, conforming to a pre-selected SC limit, and a given ductility level, at very early stages of design process. Moreover, it is shown that implementation of SCRS and FSSDOF system can be extended to account for drift limits. This is done by introducing a modified version of the “yield-point-spectra” method in which period-dependence feature of SC is recognized. Several numerical examples are included as part of the presentation.

SONOELASTOGRAPHIC FEATURES OF HIGH-RISK BREAST LESIONS AND DUCTAL CARCINOMA IN SITU - A PILOT STUDY.

SUMMARYThe aim of this study was to evaluate the quantitative sonoelastographic values recorded on shear-wave sonoelastography (SWE) of high-risk breast lesions and ductal carcinoma in situ (DCIS). We retrospectively analyzed histopathologic and SWE data (quantitative maximum, minimum and mean stiffness, lesion-to-fat ratio (E-ratio), lesion size) of 228 women referred to our Department for core needle breast biopsy during a four-year period. Among 230 lesions, histopathologic findings showed 34 high-risk breast lesions and 29 DCIS, which were compared with 167 ductal invasive carcinomas. High-risk lesions had lower values of all sonoelastographic features than ductal in situ and invasive carcinoma, however, only E-ratio showed a statistically significant difference in comparison to DCIS (3.7 vs. 6, p<0.001). All sonoelastographic features showed significant difference between in situ and invasive carcinoma. There was a significant correlation between lesion size and stiffness (r=0.36; p<0.001). Stiffness measured by SWE is an effective predictor of the histopathologic severity of sonographically detectable breast lesions. Elasticity values of high-risk lesions are significantly lower than those of malignant lesions. Furthermore, we showed that along with the sonographic appearance, which in most cases shows typical microcalcifications, DCIS had significantly different elasticity parameters than invasive carcinoma.

Minimum requirements for transverse stiffeners on orthotropic plates subjected to compression

Bridges with box cross-sections are usually stiffened by the combination of longitudinal and transverse stiffeners. The longitudinal stiffeners are loaded by axial force, and the transverse stiffeners should give sufficient support to them. The design of transverse stiffeners without direct loading can be done by the verification of the minimum stiffness requirements. It has been proved by several researchers in the past that the requirement of the EN1993-1-5 (2005) regarding the out-of-plane bending inertia of the transverse stiffeners is not on the safe side and needs further improvement. At the same time, designers have difficulties in fulfilling the torsional stiffness requirements for the transverse stiffeners using practical stiffener sections. Therefore, the current research program has the aim of harmonizing the minimum requirements for transverse stiffeners and giving applicable design proposals. Complex research strategy and advanced numerical model have been developed to determine the minimum stiffness requirement for transverse stiffeners based on bifurcation analysis and GMNI simulations. More than 3900 simulations have been executed on different geometries to investigate the structural behaviour of the longitudinally stiffened plate and the transverse stiffeners. On this basis a design method has been developed to determine the required minimum transverse stiffener.

Static analysis on a 2(3PUS+S) parallel manipulator with two moving platforms

The stiffness of a novel 2(3PUS+S) parallel manipulator with two moving platforms was investigated in this study. In the stiffness evaluation, the two moving platforms of the manipulator were driven through three linear modules and the load force on the drive joint was large. The corresponding parts of the two moving platforms were divided into independent subsystems and were integrated through a stiffness modeling method of a serial system to establish the overall stiffness model of the 2(3PUS+S) parallel manipulator. During modeling, elastic deformations on the joint lever and lead screw were involved, the joint lever was simplified as a supported beam, and the axial and torsional stiffness of the lead screw were considered. Numerical analysis on the established stiffness model was validated, and virtual experiments were conducted. Results indicate that the stiffness performance of the 2(3PUS+S) parallel manipulator changes with the variation of structural parameters and moving platform positions. To ensure the minimum stiffness under the required trajectory, the length of the joint lever and the ratio of the moving platform radius to the base platform should be appropriately reduced. Comparisons between the results from the numerical analysis and virtual experiments verified the accuracy of the established stiffness model.

A Bio-inspired Grasp Stiffness Control for Robotic Hands

This work presents a bio-inspired grasp stiffness control for robotic hands based on the concepts of Common Mode Stiffness (CMS) and Configuration Dependent Stiffness (CDS). Using an ellipsoid representation of the desired grasp stiffness, the algorithm focuses on achieving its geometrical features. Based on preliminary knowledge of the fingers workspace, the method starts by exploring the possible hand poses that maintain the grasp contacts on the object. This outputs a first selection of feasible grasp configurations providing the base for the CDS control. Then, an optimization is performed to find the minimum joint stiffness (CMS control) that would stabilize these grasps. This joint stiffness can be increased afterwards depending on the task requirements. The algorithm finally chooses among all the found stable configurations the one that results in a better approximation of the desired grasp stiffness geometry (CDS). The proposed method results in a reduction of the control complexity, needing to independently regulate the joint positions, but requiring only one input to produce the desired joint stiffness. Moreover, the usage of the fingers pose to attain the desired grasp stiffness results in a more energy-efficient configuration than only relying on the joint stiffness (i.e., joint torques) modifications. The control strategy is evaluated using the fully actuated Allegro Hand while grasping a wide variety of objects. Different desired grasp stiffness profiles are selected to exemplify several stiffness geometries.

Practical displacement-based seismic design approach for PWF structures with supplemental yielding dissipators

This paper analytically investigates the design of supplemental metallic yielding dissipators to reduce the lateral displacements of pin-supported wall-frame (PWF) structures under high-intensity ground motions. The PWF system involves the use of a base-pinned structural wall to impose a first-mode dominant lateral drift profile on the coupled frame. Supplemental dissipative devices can be applied to increase the energy dissipation capacity of the coupled system by utilizing the relative displacements at the vertical wall-to-frame connections. This study proposes a displacement-based seismic design approach to determine the dissipator parameters so that the maximum roof drift of the structure under severe ground motions can be reduced to an allowable target roof drift. The validity of the proposed approach is verified based on nonlinear dynamic time-history analyses of three PWF structures with yielding dissipators. Besides, procedures to determine the minimum wall stiffness and strength are suggested for the preliminary design of the pin-supported wall. The dynamic behaviors of the example structures are critically evaluated, indicating that PWF system is suitable for the seismic retrofit project as well as for the development of novel sustainable earthquake resisting system.

Elastic and elastic-plastic threshold stiffness of stiffened steel plate walls in compression

This paper studies the minimum stiffness required to ensure elastic buckling and elastic-plastic post-buckling strength of subpanels of vertically stiffened steel plate walls (S-SPWs) under compression. In the linear elastic analysis, the threshold stiffness at which the buckling mode of S-SPWs changes from overall to subpanel local buckling is determined. Based on the understanding that the increased elastic critical buckling strength of the S-SPW is provided by the elastic buckling resistant capacity of the stiffeners, a formula is proposed to predict the elastic threshold stiffness.The elastic-plastic threshold stiffness of vertical stiffeners, which makes the subpanels develop their full elastic-plastic post-buckling capacity, is obtained through nonlinear analysis. This paper investigated the effects of subpanel aspect ratio, subpanel width-to-thickness ratio, number of stiffeners on the elastic-plastic threshold stiffness. The effect of initial imperfection is also included. Based on the understanding that the increased capacity of the S-SPW from overall to subpanel post-buckling is provided by the elastic-plastic strength and stiffness of the stiffeners, a formula to predict the elastic-plastic threshold stiffness is proposed. The proposed formulas for both threshold stiffness are found to possess good accuracy after some minor modifications. The comparison between elastic and elastic-plastic threshold stiffness is also presented.