Prestressed State Research Articles

Force finding of cable–strut structures using a symmetry-based method

Force finding of cable–strut structures is to identify self-equilibrated pre-stress states for structures with given shape, which is a crucial step in the structural design of flexible structures since pre-stresses significantly affect their mechanical behaviors. Utilizing symmetry properties of structures is generally considered as a practical way to facilitate the force finding process. To indicate the symmetric feature of structures, an algebraic indicator is proposed in the context of the equilibrium matrix theory. Furthermore, it is found that the orthogonal projection onto the null space of the equilibrium matrix could show the symmetry properties of structures geometrically. Then, a symmetry-based method of computing feasible pre-stress states is developed in the light of the above orthogonal projection. Finally, the proposed method is applied on three examples to confirm its validity and accuracy.

Calculation of the effective properties of the prestressed nonlinear elastic heterogeneous materials under finite strains based on the solutions of the boundary value problems using finite element method

This paper describes the approach and algorithms for numerical estimation of the effective properties of the prestressed nonlinear elastic heterogeneous materials under finite strains. To numerically evaluate effective properties on a representative volume (or periodicity cell), a series of sequences of elasticity problems differing in the type of the applied boundary conditions is solved. In all the problems being solved, along with the specially applied boundary conditions, the model undergoes the same predetermined prestress. In addition, a separate problem is being solved, in which, besides the prestressed state, zero displacement of the model boundary are set. The results of solving each problem in the form of stress tensors are averaged over the volume. Numerical calculations were carried out using the Fidesys Composite software module of the Fidesys CAE system using the finite element method. The paper presents the solution to a number of problems to estimate the effective coefficients of the porous material prestressed by pore pressure. Dependence graphs of effective properties on porosity and on size of pore pressure are constructed.

Prestress tuning of negative refraction and wave channeling from flexural sources

The quest for wave channeling and manipulation has driven a strong research effort on topological and architected materials, capable of propagating localized electromagnetical or mechanical signals. With reference to an elastic structural grid, the elements of which can sustain both axial and flexural deformations, it is shown that material interfaces can be created with structural properties tuned by prestress states to achieve total reflection, negative refraction, and strongly localized signal channeling. The achievement of a flat lens and topologically localized modes is demonstrated, and the tunability of the system allows these properties to hold for a broad range of wavelengths. An ingredient to obtain these effects is the use, suggested here and never attempted before, of concentrated pulsating moments. The important aspect of the proposed method is that states of prestress can be easily removed or changed to tune with continuity the propagational characteristics of the medium, so that a new use of vibration channeling and manipulation is envisaged for elastic materials.

The role of material and geometric nonlinearities in acoustoelasticity

Wave propagation in prestressed and prestrained continua can be modelled by the theory of acoustoelasticity, which typically includes different assumptions. These are third or fourth order expressions of hyperelastic strain energy, as well as finite initial strains and a formulation of balance equations in the current configuration. In this paper, we use a model describing wave propagation in a three dimensional elastically prestrained continuum to clarify the role of different mechanical aspects taken into account in the classical hypotheses of the theory. We consider different states of prestress: hydrostatic, biaxial and uniaxial. Changes in shear and longitudinal wave speeds and their polarization as a function of the initial prestress are described for all directions of propagation. The role of the strain energy power order in changes of speed is elucidated. Moreover, material and geometric nonlinearities are shown to affect changes with the opposite sign, depending also on the direction of propagation.

Dynamic Mechanical and Fracture Behaviour of Sandstone Under Multiaxial Loads Using a Triaxial Hopkinson Bar

Variations in stress conditions of rocks have been observed during blasting for excavation or large-scale seismic events such as an earthquake. A triaxial Hopkinson bar is developed to apply initial pre-stresses achieving various in situ stress conditions, including uniaxial (principal stresses σ1 > σ2 = σ3 = 0), biaxial (σ1 ≥ σ2 > σ3 = 0) and triaxial (σ1 ≥ σ2 ≥ σ3 ≠ 0) confinements, and then to determine properties of materials under multiaxial pre-stress states at high strain rate. A series of tests was conducted on sandstone specimens to investigate dynamic responses under multiaxial pre-stress states. A high-speed camera at the frame rate of 200,000 fps with a resolution of 256 × 256 pixels was used to capture the fracture characteristics rocks under biaxial compression tests. Experiments show that under the same impact velocity, dynamic properties (e.g. dynamic strength, elastic modulus, fracture modes) of sandstone exhibit confinement dependence. Dynamic strength decreases with increasing axial pre-stress σ1 along the impact direction, while it increases with the increase of lateral pre-stresses σ2 and σ3. The elastic modulus increases with the confinement varying from uniaxial, biaxial to triaxial compression. Rocks are pulverised into powder under uniaxial pre-stress impact, and fragments are ejected from the free face under biaxial compression, while they show slightly damaged or a macroscopic shear fracture under triaxial compression. The 3D imaging of fracture networks in the damaged/fractured specimens was acquired via the X-ray computed tomography system.

Modeling and frequency analysis of prestressed functionally graded plates with holes

Materials with complex inhomogeneous structure, including functionally graded composites, are widely used in military and civil engineering, and in modern construction. Due to the peculiarities of the technological process of manufacturing such materials, in many of them a non-uniform initial stress-strain state develops. At the same time, in the production, prestress fields are often embedded in structures to improve their strength characteristics. This paper presents a general linearized formulation of the problem on oscillations of a prestressed elastic body. Using it as a basis, we have formulated the problem on steady-state mixed vibrations of a functionally graded perforated plate in a prestressed state within the framework of Timoshenko deformation hypotheses. A numerical solution to the direct problem was constructed using the finite element method; the effect of the inhomogeneous prestressed state of the plate on its amplitude-frequency characteristics and resonant frequencies was investigated. The results of computational experiments for the functionally graded laws for material modules simulating the W-Cu alloy are given. In the zones of circular plate holes, we used the local condensation of the finite element mesh to increase the accuracy of calculations. The proposed model allows to set an arbitrary type of initial state in the plate, both in the form of analytical dependencies and numerically. We present an example of a numerical experiment, when stress fields were formed in a plate as a result of applying some initial mechanical static load to a part of its boundary. In order to describe such a stress field, the corresponding static problem for the plate under consideration was additionally solved. The possibilities of identifying the parameters of a plane prestressed state based on the acoustic measurement data on the frequency characteristics of the plate are investigated

Effect of Static Loads on the Natural Vibrations of Ribbed Shells

The article is devoted to a further analysis of the natural vibrations of inhomogeneous shells under the action of static loads. The method of investigation is based on a unified methodology that combines the problems of static stability and the vibrations of elastic shells. The problems of natural vibrations take into account the presence of a prestressed state of the shell structure from the action of static loads. The presence of a static load significantly affects the spectrum of the natural frequencies of the shell. This approach allows us to determine the critical load by the dynamic criterion.The method of investigating of inhomogeneous shells is based on the uniform methodological positions of the 3-d geometrically nonlinear theory of thermoelasticity and the finite-element method in the form of the moment finite-element scheme. So, a thin shell is considered by this method as a three-dimensional body which is modeled throughout the thickness by one isoparametric solid finite element with multilinear shape functions.Two nonclassical hypotheses are used to describe the stress–strain state of a thin inhomogeneous shell. The kinematic hypothesis of deformed straight line in the thickness direction: though stretched or shortened during deformation, a straight segment along the thickness remains straight. This segment is not necessarily normal to the mid-surface of the shell. The displacements are assumed distributed linearly along the thickness, which is conventional in the theory of thin shells. The static hypothesis compressive assumes that the stresses in the fibers are constant throughout the thickness of the shell.Modal analysis of a shallow ribbed panel demonstrates the effectiveness of the developed method. The natural frequencies and mode shapes are determined at each increment of static loading.

Single-Molecule Study of Peptide Gel Dynamics Reveals States of Prestress.

De novo peptide surfactant (I3K) gels provide an ideal system to study the complex dynamics of lightly cross-linked semiflexible fibers because of their large contour lengths, simple chemistry, and slow dynamics. We used single-molecule fluorescence microscopy to record individual fibers and Fourier decomposition of the fiber dynamics to separate thermal contributions to the persistence length from compressive states of prestress (SPS). Our results show that SPS in the network depend strongly on peptide concentration, buffer, and pH and that the fibril energies in SPS follow a Lévy distribution. The presence of SPS in the network imply that collective states of self-stress are also present. Therefore, semiflexible polymer gels need to be considered as complex load-bearing structures and the mean field models for polymer gel elasticity and dynamics often applied to them will not be fully representative of the behavior at the nanoscale. We quantify the impact of cross-links on reptation tube dynamics, which provides a second population of tube fluctuations in addition to those expected for uncross-linked entangled solutions.

Motion characteristics of a vibration driven mobile tensegrity structure with multiple stable equilibrium states

A novel type of a vibration driven motion system based on a compliant tensegrity structure with multiple stable equilibrium states is considered. These equilibrium configurations correspond to different prestress states with different dynamical properties. Therefore, the motion characteristics can be varied by changing the equilibrium state. For the application in the fields of mobile robotics, these discrete adjustable dynamics are advantageous. The vibration modes of the structure as well as the corresponding motion characteristics of the system can be adapted to the given environmental conditions in order to ensure a reliable motion. In this paper, dynamical investigations of an exemplary two-dimensional multistable tensegrity structure are considered. For the chosen parameter values the structure features two relevant equilibrium configurations. The resulting motion system is in contact to a horizontal plane due to gravity and the actuation is realized by the harmonic variation of the length of a single tensioned member. The motion of the system is simulated for various actuation frequencies with the different equilibrium states as an initial configuration. A uniaxial or a planar movement occurs depending on the selection of the actuated member within the tensegrity structure. The steady state motion is evaluated regarding motion characteristics like the steady state velocity. Moreover, the influences on the motion behavior caused by the different equilibrium states as an initial condition are emphasized.

Generation of planar tensegrity structures through cellular multiplication

Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

On decoding the structural behaviour of hybrid cable bending-active units in fastening, prestress and load-bearing state

This article examines the structural behaviour of six structural units composed of single, simply paired and paired-interconnected bending-active members, coupled with a single cable element. The form-found curvilinear shape of the members is achieved through fastening by contracting auxiliary elements, as well as through further deformation by decreasing the cable’s length. The overall structural behaviour of the units is investigated based on a step-by-step finite-element analysis. All units are evaluated with regard to the components’ stresses and deformations developed during the form-finding process and subsequent external vertical loading, for different possible section thickness values of the elastic members.

A modular inverse elastostatics approach to resolve the pressure-induced stress state for in vivo imaging based cardiovascular modeling

Patient-specific biomechanical modeling of the cardiovascular system is complicated by the presence of a physiological pressure load given that the imaged tissue is in a pre-stressed and -strained state. Neglect of this prestressed state into solid tissue mechanics models leads to erroneous metrics (e.g. wall deformation, peak stress, wall shear stress) which in their turn are used for device design choices, risk assessment (e.g. procedure, rupture) and surgery planning. It is thus of utmost importance to incorporate this deformed and loaded tissue state into the computational models, which implies solving an inverse problem (calculating an undeformed geometry given the load and the deformed geometry). Methodologies to solve this inverse problem can be categorized into iterative and direct methodologies, both having their inherent advantages and disadvantages. Direct methodologies are typically based on the inverse elastostatics (IE) approach and offer a computationally efficient single shot methodology to compute the in vivo stress state. However, cumbersome and problem-specific derivations of the formulations and non-trivial access to the finite element analysis (FEA) code, especially for commercial products, refrain a broad implementation of these methodologies. For that reason, we developed a novel, modular IE approach and implemented this methodology in a commercial FEA solver with minor user subroutine interventions. The accuracy of this methodology was demonstrated in an arterial tube and porcine biventricular myocardium model. The computational power and efficiency of the methodology was shown by computing the in vivo stress and strain state, and the corresponding unloaded geometry, for two models containing multiple interacting incompressible, anisotropic (fiber-embedded) and hyperelastic material behaviors: a patient-specific abdominal aortic aneurysm and a full 4-chamber heart model.

Experimental study on wheel-spoke crossed cable structures

Wheel-spoke crossed cable structure is a new type of cable-strut structure. In this article, the tension forming and static performance of wheel-spoke crossed cable structure are experimentally investigated by testing four scale models under full-span and half-span downward uniform load, and the effect of structural parameters including variable prestress level, height difference between inner ring and outer ring, and layer height of inner ring is studied by finite element method as well. The test results indicate that radial cables tensioning scheme is effective for wheel-spoke crossed cable structure to reach initial prestress state, and wheel-spoke crossed cable structure possesses excellent load-carrying capacity and structural stiffness since internal forces and vertical displacements of models vary almost linearly under such load cases. Moreover, the static test results are in good agreement with the finite element analysis results, confirming that the model design, measurement methods, and loading schemes are reasonable. Therefore, the results of this study can provide valuable reference for the design and application of wheel-spoke crossed cable structure.

Determination of the Inhomogeneous Preliminary Stress–Strain State in a Piezoelectric Disk

The problem of steady radial vibrations of a thin electroelastic hollow disk in the presence of a preliminary inhomogeneous plane stress–strain state is solved. Vibrations are induced by applying a potential difference across the electrodes placed on the end surfaces of the disk. Equations of the vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lam´e problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining a pre-stress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial data specified with an error is analyzed.

Variation simulation model for pre-stress effect on welding distortion in multi-stage assemblies

In the shipbuilding industry, steel plates are assembled and joined to construct a block, and dozens of blocks are erected to build a ship. The major joining process used to assemble the steel plates is welding. Because the welding process causes strong non-uniform heating of the parts being joined, the local heating and subsequent cooling of welded pieces induce volumetric changes, producing transient and residual stresses as well as plastic deformation. This welding distortion is the main factor causing geometrical imperfections in the steel plate assembly process. These non-nominally shaped parts need to be clamped before the following joining process, which in turn causes pre-stress in the parts being joined. The pre-stresses due to welding and clamping significantly affect the subsequent welding processes. This paper proposes a variation simulation model of compliant assemblies to analyze the propagation of geometrical variations through multiple assembly stages, including the welding distortion under the effect of the pre-stress state. This research extends the mechanical variation simulation model to include the effects of clamping stresses by expressing the pre-stress terms in the form of an additional stiffness matrix. The result helps in confirming the effect of the pre-stress state on the subsequent welding distortion in the multi-stage assembly process. The proposed model can be used to predict the propagation of assembly variation in steel plate assemblies considering the pre-stress effect and welding distortion.

Epigenomics of Plant Responses to Environmental Stress

Genome-wide epigenetic changes in plants are being reported during development and environmental stresses, which are often correlated with gene expression at the transcriptional level. The sum total of the biochemical changes in nuclear DNA, post-translational modifications in histone proteins and variations in the biogenesis of non-coding RNAs in a cell is known as an epigenome. These changes are often responsible for variation in the expression of the gene without any change in the underlying nucleotide sequence. The changes might also cause variation in chromatin structure resulting in the changes in function/activity of the genome. The epigenomic changes are dynamic with respect to the endogenous and/or environmental stimuli, which affect phenotypic plasticity of the organism. Both the epigenetic changes and variation in gene expression might return to the pre-stress state soon after the withdrawal of the stress. However, a part of the epigenetic changes may be retained, which is reported to play a role in acclimatization and adaptation as well as in the evolutionary process. Probable exploitation of epigenome-engineering for improved stress tolerance in plants has become essential for better utilization of the genetic resources. This review delineates the importance of epigenomics towards the possible improvement of plant responses to environmental stresses for climate resilient agriculture.

Incremental auxetic response of composite lattices under isotropic prestress

This work studies the constitutive response of two- and three-dimensional lattice materials subject to isotropic prestress, with a focus on the elastic stiffness moduli that can be directly measured through experimental tests. The elementary unit cell of the examined lattices is formed by an arbitrary number of junctions attached to a junction. Analytic formulae for the elastic stiffness coefficients of stretching-dominated lattices are provided. In addition, numerical results for the incremental elastic moduli of composite lattices equipped with hard and soft rods are presented. The given results highlight that isotropically pre-tensioned lattices may exhibit marked variations of the elastic stiffness moduli in the prestressed state, over the values competing to the stress-free configuration. This study also discloses that prestressed lattices may feature incremental auxetic response, when composite architectures suitably combining hard and soft materials are employed for their fabrication.

Dispersion curves for Lamb wave propagation in prestressed plates using a semi-analytical finite element analysis.

Acoustoelastic techniques have been recently used to characterize the state of prestress in structures such as plates. The velocity of guided wave modes propagating through plates is sensitive to the magnitude and orientation of the initial state of stress. Dispersion curves for phase velocities of plate guided waves can be computed using the superposition of partial bulk waves (SPBW) method. Here, a semi-analytical finite element (SAFE) method is formulated for the acoustoelastic problem of guided waves in weakly nonlinear elastic plates. The SAFE formulation is shown to provide phase velocity dispersion curve results identical with those provided by the SPBW method for the problem of a plate under a uniaxial and uniform tensile stress. Analytical phase and group velocity dispersion curves are also obtained for a plate with an initial prestress gradient through its thickness using the SAFE method. The magnitude of the prestress gradient is shown to have a significant effect on phase and group velocities of the fundamental and first order Lamb modes, only in certain frequency-thickness regimes.

Influence of prestressed state on frequencies of hydroturbine bearing structures

Метою роботи є створення методики розрахунку власних частот коливань кришки гідротурбіни у вакуумі та при взаємодії з водою з урахуванням попередньо напруженого стану конструкції. Задача розв'язується методом скінченних елементів і полягає у знаходженні частот та форм коливань. Вплив інерційних сил від мас та устаткування, яке розташоване на кришці, враховується приведеною густиною. Також у динамічному процесі враховується вплив рідини. Попередньо напружений стан моделюється шляхом введення так званої геометричної матриці жорсткості, яка одержана на основі тензора попередніх напружень і нелінійної частини тензора деформацій. Розв'язана задача з визначення частот власних коливань сталевої циліндричної оболонки, що знаходиться під дією внутрішнього тиску. Для вибору розміру скінченного елемента виконана серія розрахунків і проведена оцінка збіжності розв'язку. Встановлено, що внутрішній тиск приводить до збільшення власних частот коливань циліндричної оболонки, а зовнішній їх знижує. На тестовому прикладі перевірена роботоспроможність запропонованого підходу і підтверджено достовірність результатів, отриманих на його основі. Результати, отримані за розробленим підходом, відрізняються від експериментальних даних від 0,5 до 11%. На основі запропонованого підходу досліджені вільні коливання кришки гідротурбіни, що виготовлена з листового прокату сталі.

Direct and inverse problems for prestressed functionally graded plates in the framework of the Timoshenko model

In this study, modelling and identification of prestress state in functionally graded plate within the framework of the Timoshenko theory are discussed. With the help of variational principles, statements of boundary problems for stationary vibration of inhomogeneous prestressed plates have been derived taking into account various factors of prestress state. The comparative analysis of classical and nonclassical models has been conducted. The effect of the prestress state factors on the solution characteristics has been estimated. New approaches to solving the inverse problems on a reconstruction of inhomogeneous prestress functions in a functionally graded plate have been proposed on the basis of derivation of reciprocity relations and iterative regularization. The results of numerical reconstruction experiments are presented; practical recommendations on a selection of frequency range for the purpose of getting the highest reconstruction accuracy are given.