Initial Static Loading Research Articles

Use of the finite elements method for modelling the dynamic load impact on hydraulic leg equipped with gas accumulator

Procedures of preparation of numerical analysis, consisting in a simulation of cooperation of three different media: steel, liquid and gas undergoes dynamic load were discussed. Modelling of the initial static load of the mechanical system was presented. By using the MSC. Software products the following exemplary computer simulations were made: dynamic load impact on the hydraulic leg as well as effectiveness of the hydraulic leg protection against overload with help of gas accumulator.

Influence of initial static stress on the dynamic properties of concrete

Abstract Concrete structures prior to being subjected to dynamic loadings such as earthquake have already withstood initial stress. So the study of strain-rate sensitivity of concrete should be closely related to the initial loading history that concrete experiences. Yet majority of available documents concerning the dynamic properties of concrete do not take the initial static loading history into consideration. In this study, experiments were carried out to investigate the effect of initial static stress on the dynamic strength and deformation characteristics of concrete. A prescribed load was initially applied on the specimen at a very low strain-rate and then a dynamic load was applied at a high strain-rate up to failure of the specimen. The relationship between dynamic strength factor and the initial stress is obtained. The comparison between the results by the proposed formula and those by experiments in this study indicates a good agreement. The stress–deformation curves obtained in the tests show that the initial static loading history plays an important role in the total deformation behavior of concrete. An explanation to the physical mechanisms of high strain-rate strength enhancement with different initial static stress was proposed.

Rate effect of concrete strength under initial static loading

The dynamic strength enhancement of concrete under different initial static loadings is investigated in this paper. The mechanism of the influence of the inertia effect on the dynamic strength of concrete is discussed first by analyzing a single dimension of freedom system, which shows that the inertia effect only influences the dynamic loading part. The dynamic strength of concrete at initial static loading is calculated assuming a single crack model with consideration of free water viscosity using dynamic fracture mechanics. The dynamic stress intensity factor of the crack under linearly increasing loading on the basis of an initial static loading is achieved. The relationship between the dynamic strength increase factor and the static stress level is obtained. The comparison between the results by the model proposed in this paper and those by experiments in some available references indicates a good agreement.

Response of Concrete to Dynamic Elevated-Amplitude Cyclic Tension

A universal testing machine was used to test the behavior of concrete subjected to cyclically varying load whose amplitude was constantly increasing. How concrete's dynamic strength has been affected by the rate of amplitude increment per loading cycle, cycle frequency, and initial static loading intensity has been studied. It was found that in concrete subjected to cyclically varying loading's strength enhancement, an important role was played by each cycle maximum loading rate in the frequency range of earthquake excitation. The amplitude increment rate's influence is insignificant. The authors present a formula for strength enhancement prediction of concrete which has been subjected to cyclically varying load based on monotonic loading test results. That concrete subjected to carrying cyclic loading's strength enhancement showed a tendency, with increasing initial static loading, to decrease, was revealed through experimental results. Unrecoverable plastic deformation magnifies along with loading cycle growth.

Effect of Initial Static Load on the Rate-Sensitive Behavior of Concrete in Compression

Before concrete structures are subjected to dynamic loadings such as earthquake, usually they have already withstood static loads. Accordingly, the study on the strain-rate sensitivity of concrete should also be closely related to the initial static loads that concrete structures experience. But majority of the available documents concerning the dynamic properties of concrete do not take initial static load into consideration. In this study, experiments were carried out to investigate the effect of initial static load on the dynamic strength and deformation characteristics of concrete in compression. A load was initially applied on the specimen at a very low speed to a specified value and then the dynamic load was applied at a high strain rate up to the failure of the specimen. From the test results it was revealed that the initial static load had significant influence on the dynamic strength. The dynamic strength tended to decrease as initial static load increased. An exponential function was proposed to formulate the relationship between the initial static load and the dynamic strength.

Dynamic response and failure behavior of rock under static-dynamic loading

Dynamic response and failure behavior of rock under static-dynamic loading were studied. The effects of initial static load on the total energy dissipated during the failure process of specimen were analyzed. To simulate the engineering situation that in-situ rock experienced and obtain the dynamic loading with an intermediate strain rate, a low cycle fatigue load with the frequency from 0.5 to 5 Hz was adopted by servo-controlled Instron material testing system. The results show that the obtained strain rate increase with the increase of load frequency. The initial static load has great influence on both the energy and dynamic response of rock. Both the energy and the maximum failure load P f decreases with the increase of initial static load. P f under the static-dynamic loading is larger than that under only the static loading but less than that under only the dynamic loading. The load-displacement curves become nonlinear as the pre-added static load reaches the transition point which is about one third of static strength. With the increase of initial static load, Young’s modulus decreases and poisson ratio increases. It shows that rock has a lower strength and a tendency to soften under a higher initial static load. Rock may be broken more easily static-dynamic loading than under only the dynamic loading. The proposed method is useful in the investigation of constitutive relationship and failure behavior of rock under quasi-dynamic loading.

Static and dynamic simulation of a 700-m high rock slope in western Norway

Static and dynamic rock slope stability analyses were performed using a numerical discontinuum modelling technique for a 700-m high rock slope in western Norway. The rock slope has been investigated by the Geological Survey of Norway (NGU), which has been carrying out rock slide studies for the county Møre and Romsdal in western Norway. The purpose of numerical modelling was to estimate the volume of the rock mass that could potentially slide under static and dynamic forces. This estimation was required to assess the run-up heights (tsunami) in a fjord that could potentially be caused by the rockslide. Three cases have been simulated for predicting the behaviour of the rock slope. First, an initial static loading is applied in the numerical model to simulate the prevailing rock mass conditions at the site. Second, saturated and weathered joint conditions are modelled by reducing the residual friction angle along the discontinuities of the rock mass. In doing so, the model simulates the effect of degradation of discontinuities in the rock slope. Third, a dynamic loading, based on peak ground accelerations expected in the area, is applied to simulate dynamic earthquake conditions. These numerical studies have provided some useful insights into the deformation mechanisms in the rock slope. Both sliding and rotation of blocks start to occur once the residual friction angle along the discontinuities is reduced and when the region is shaken by a strong earthquake. The results indicate that, due to variations in the inclination of discontinuities, the entire slope does not become unstable and that down-slope sliding and rotation of blocks occur mainly on the top layers of the slope. Within the range of parameter values considered for this study, it is unlikely that the whole rock slope can be destabilised. The study provides an illustration of how the geo-mechanical properties of a rock mass can be integrated in a discontinuum rock slope model, which is used for predicting the behaviour of the slope under existing environmental and earthquake conditions. This model has helped not only to better understand the dynamics of the rockslide but also to estimate the potential rock volume that can become unstable when subjected to static and dynamic loads.

Nonlinear vibration and dynamic response of simply supported shear deformable laminated plates on elastic foundations

Nonlinear vibration and dynamic response are presented for a simply supported, shear deformable laminated plate subjected to a transverse dynamic load combined with initial in-plan static loads and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy’s higher order shear deformation plate theory and general von Kármán-type equation, which includes the plate-foundation interaction. Two cases of the in-plane boundary conditions are considered. The equations of motion are solved by means of a perturbation technique to determine nonlinear frequencies and dynamic responses of symmetric cross-ply and antisymmetric angle-ply shear deformable laminated plates. The effects of amplitude ratio, foundation stiffness and initial in-plane loads on frequency ratios and dynamic responses are also studied. The results show that the foundation stiffness and initial in-plane loads have a significant effect on the nonlinear to linear frequency ratios as well as dynamic response of shear deformable laminated plates.

Experimental flatfoot model: the contribution of dynamic loading.

The goal of this study was to determine if the application of muscle forces (simulating the dynamic phase of the midstance part of gait) had an effect on flatfoot deformity. We created a flatfoot model in each of seven cadaver foot specimens by grasping the Achilles, peroneus longus, peroneus brevis, flexor digitorum longus, and flexor hallucis longus tendons with soft-tissue vice clamps connected via wire cables to pneumatic cylinders. The experiment included four stages: 1) initial static axial loading; 2) axial loading after 3,000 load cycles (average, 735 N; range, 70 to 1400 N); 3) axial loading after releasing the spring ligament and plantar fascia; and 4) axial loading after an additional 3,000 load cycles. At each stage, both static (with axial loading only) and dynamic (axial loading with tensioning of the tendons to simulate the muscle forces at midstance) conditions were evaluated radiographically. No change was observed between the static and dynamic conditions in the first two phases of the experiment. After the third phase, changes in the talar-first metatarsal angle and the height of the medial cuneiform were noted, particularly in the dynamic condition. These and additional radiographic changes were magnified in the fourth phase, but only in the dynamic condition. We concluded that, to create an effective flatfoot model, the medial structures, including the spring ligament and possibly the plantar fascia, must be severed. Cyclic loading of the foot further increased the arch flattening, and this effect was magnified by dynamic loading.

Classical and Nonclassical Dynamic Problems of Sandwich Shells with a Transversely Soft Core

Based on the hypothesis of similarity of transverse displacements in thin-walled sandwich shells with a transversely soft core under dynamic and static loads, refined geometrically nonlinear dynamic equations of motion are constructed in the case of large variations in the parameters of the stress-strain state (SSS) in the tangential directions. For shells structurally symmetric across the thickness and loaded with initial static loads, linearized dynamic equations are derived, which, upon introducing the synphasic and antiphasic functions of displacements and forces, can be used to describe the synphasic and antiphasic buckling forms in the transverse and tangential directions. For nonshallow cylindrical and shallow spherical shells, the nonclassical problems on all possible vibration forms realized at zero indices of variability of the SSS parameters in the tangential directions are formulated and solved. For shallow shells of symmetric structure, the resolving equations are obtained by introducing, instead of tangential displacements and transverse tangential stresses in the core, the corresponding potential and vortex functions.

Simultaneous Optimum Design of Structural and Control Systems for Truss Structure.

This paper proposes an optimum design problem of structural and control systems, taking a 2-D truss structure as an example. The structure is supposed to be subjected to initial static loads and disturbances. For the structure, FEM model is formed, and using modal transformation, the equation of motion is transformed into that of modal coordinate in order to decrease DOF of FEM model. The structure is controlled by an output feedback H∞ controller to suppress the effect of the disturbances. The design variables are the cross sectional areas of truss members. The structural objective function is the structural weight. As the control objective, we consider two types of performance indices. The first function is the H∞ norm, that is, the performance index for disturbance suppression. The second one is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been carried out. Through the consideration of structural weight and H∞ norm, an advantage of the simultaneous optimum design of structural and control systems is shown. More-over, while the performance index of control is almost kept, we can perform the design which is better also in structural strength.

Woven composite design for extreme events using a damage mechanics methodology

Current predictive techniques for the analysis of composite structures and components near and beyond their ultimate strength are simplistic, using basic failure functions and traditional failure envelopes to determine the degree of damage in some arbitrary composite component or structure subjected to a biaxial or triaxial loading regime. Similarly, the design procedure usually assumes that the composite structure remains elastic throughout any potential applied loading. The analysis methodology proposed in this paper reflects a state-of-the-art dynamic modelling technique based on finite elements (FE) that can be used to model a wide range of problems, from extreme events, such as an explosion, to non-linear static problems that can occur near discontinuities or free edges. The damage mechanics approach presented in this paper uses a scalar damage variable assigned to each observed damage mode. As damage is cumulative and related to the engineering constants, such as the Young's modulus, the technique allows initial and/or post-dynamic static loads to be applied to the composite structure or component, so potentially a cradle-to-grave composite design methodology could be developed. The forms of the stress-strain curve for woven glass composite and the relevance of experimentally measured material damage constants are discussed. The proposed damage mechanics approach has been implemented as a new material failure model in the explicit dynamic DYNA3D FE code. Results are presented for two high-velocity (bird strike) impact events on a woven glass composite.

Woven composite design for extreme events using a damage mechanics methodology

Current predictive techniques for the analysis of composite structures and components near and beyond their ultimate strength are simplistic, using basic failure functions and traditional failure envelopes to determine the degree of damage in some arbitrary composite component or structure subjected to a biaxial or triaxial loading regime. Similarly, the design procedure usually assumes that the composite structure remains elastic throughout any potential applied loading. The analysis methodology proposed in this paper reflects a state-of-the-art dynamic modelling technique based on finite elements (FE) that can be used to model a wide range of problems, from extreme events, such as an explosion, to non-linear static problems that can occur near discontinuities or free edges. The damage mechanics approach presented in this paper uses a scalar damage variable assigned to each observed damage mode. As damage is cumulative and related to the engineering constants, such as the Young's modulus, the technique allows initial and/or post-dynamic static loads to be applied to the composite structure or component, so potentially a cradle-to-grave composite design methodology could be developed. The forms of the stress-strain curve for woven glass composite and the relevance of experimentally measured material damage constants are discussed. The proposed damage mechanics approach has been implemented as a new material failure model in the explicit dynamic DYNA3D FE code. Results are presented for two high-velocity (bird strike) impact events on a woven glass composite.

Vibration analysis of pre-stressed pressure sensors using finite element method

The dynamic properties of a pre-stressed string-plate sensor are studied using the finite element method. The string-plate sensor is made of a thin circular plate, subjected to initial in-plane uniform tension and transverse static pressure, and a pre-stretched string. The geometrical nonlinearity of the plate is included in the analysis. Two-step analysis procedure is involved. A wide range of numerical results are presented. Influences of the geometrical parameters and initial static loads on the dynamic behavior of the string-plate sensor are discussed, which are very useful for design of this kind of sensor.

Modelling crack propagation in structural adhesives under external creep loading

Abstraet-Bulk adhesive compact tension specimens have been subjected to creep loads which range from 45% to 80% of the initial static failure load. Measurements of crack growth, load-line displacement, and crack tip profile were taken. Tensile creep tests were carried out on the same material and the results were used to generate material models for the analytical solution of steady-state power law (SSPL) creep and the numerical (finite element analysis) solution which incorporates the transient and primary creep material behaviour. Standard solutions for SSPL creep of compact tension specimens were used to calculate fundamental parameters such as the C* integral, creep zone growth, and transition time. From these data it would seem likely that the crack growth is controlled by creep, rather than elastic, singular fields. Crack driving parameters from both elastic and creep fields appear equally valid but the latter appear more discriminating. Finite element analyses were carried out for both a stationary crack and a propagating crack. The former are relevant to the incubation period and allow the redistribution of stress and accumulation of creep strain to be assessed. The latter enable the predicted conditions in the domain surrounding the propagating crack to be investigated for appropriate crack driving parameters. There is strong evidence to suggest that the adhesive uni-axial creep rupture strain can be successfully used to predict creep crack growth.

Tests on Model Jacked Piles in Calcareous Sand

Abstract This paper presents the results of a series of displacement-controlled cyclic axial loading tests of model jacked piles in dry calcareous sand. The tests were conducted using a large test facility comprising a test chamber 1.0 m in internal diameter and 1.55 m in height. Model instrumented aluminum jacked piles 50 and 100 mm in diameter were used to investigate scale effects on the degradation of skin friction capacity under cyclic loading conditions. Test results are presented for the response during jacking (installation), initial static compression loading, cyclic loading, and post-cyclic static compression loading response. It is shown that the degradation of skin friction is governed by the “cyclic slip displacement” model.

Instability of cylindrical panels under combined static and dynamic loads

This paper presents a numerical study of the dynamic snap-through instability of cylindrical panels subjected to the combined loading of uniform pressure and a central concentrated load. All static and dynamic (sudden step load) combinations of the concentrated load and the uniform pressure are considered. The characteristics of the dynamic instability of the panel are described for the two cases of static pressure with dynamic concentrated load and dynamic pressure with static concentrated load. The critical load curves for both cases are presented. To explain the effects of the initial static loads on the critical dynamic loads, the static and dynamic critical loads corresponding to both static loads or both dynamic loads are also calculated. The Budiansky-Roth criterion is employed in all these studies to determine the critical dynamic loads. The numerical results show that the static critical load curve gives an upper-bound whereas the dynamic critical load curve offers a lower-bound. Both the compound critical load curves lie between the static and dynamic critical load curves.

Vibrations of Planar Curved Beams, Rings, and Arches

This work attempts to organize and summarize the extensive published literature on the vibrations of curved bars, beams, rings and arches of arbitrary shape which lie in a plane. In-plane, out-of-plane and coupled vibrations are considered. Various theories that have been developed to model curved beam vibration problems are examined. An overview is presented of the types of problems which are addressed in the literature. Particular attention is given to the effects of initial static loading, nonlinear vibrations and the application of finite element techniques. The significantly different frequencies arising from curved beam theories which either allow or prevent extension of the centerline during vibratory motion are shown. An extensive bibliography of 407 relevant references is included.

Structural Modal Multifurcation With International Resonance: Part 1—Deterministic Approach

The bifurcation and multifurcation in multimode interaction of nonlinear continuous structural systems is investigated. Under harmonic excitation the nonstationary response of multimode interaction is considered in the neighborhood of fourth-order internal resonance condition. The response dynamic characteristics are examined via three different approaches. These are the multiple scales method, numerical simulation, and experimental testing. The model considered is a clamped-clamped beam with initial static axial load. Under certain values of the static load the first three normal modes are nonlinearly coupled and this coupling results in a fourth-order internal resonance. The method of multiple time scales yields nonstationary response in the neighborhood of internal resonance. Within a small range of internal detuning parameter the third mode, which is externally excited, is found to transfer energy to the first two modes. Outside this region, the response is governed by a unimodal response of the third mode which follows the Duffing oscillator characteristics. The bifurcation diagram which represents the boundaries that separate unimodal and mixed mode responses is obtained in terms of the excitation level, damping ratios, and internal resonance detuning parameter. The domains of attraction of the two response regimes are also obtained. The numerical simulation of the original equations of motion suggested the occurrence of complex response characteristics for certain values of damping ratios and excitation amplitude. Both numerical integration and experimental results reveal the occurrence of multifurcation as reflected by multi-maxima of the response probability density curves.

Characterization of Fatigue Behavior in Quasi-Isotropic Laminate of Ceramic Composite

Fatigue damage mechanisms in a quasi-isotropic laminate, [0/ 2 45/90] s of silicon carbide fiber reinforced calcium-alumino-silicate glass ceramic composite was investigated. Several tests were conducted at different maximum stress levels which intro duced varying degree of initial matrix cracking in 90°, 45° and 0° plies. The initial damage and change in modulus was monitored during the fatigue cycling. Specimens with a considerable amount of initial cracking in 0° plies failed in less than 700 cycles, and others did not fail over one million cycles. The results of this study confirmed the findings of the previous studies regarding the existence of fatigue limit in ceramic composites. The fatigue limit did not correspond to the proportional limit of the static test as reported in the previous studies, however, it corresponded to the initial damage or static loading condition where 0° plies were largely intact.