A computationally efficient shear deformable beam element for large deformation multibody applications

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The accompanying defects of the phenomenon known as shear locking are avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples, and the results are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

Absoluuttisten solmukoordinaattien menetelmä kuorimaisten kappaleiden mallinnuksessa

Työn tavoitteena oli kehittää nopeasti konvergoiva kuorielementti epälineaarisesti joustavien kappaleiden analysointiin. Kuorielementti perustuu absoluuttisten solmukoordinaattien menetelmään ja se hyödyntää kaarevuuden kuvausta elastisten voimien määrityksessä. Kehitettyä elementtiä verrattiin kontinuumimekaniikalla kehitettyyn kuorielementtiin ja kaupallisen elementtimenetelmän kuorielementtiin. Yksinkertaisimman kuormitustapauksen tuloksia verrattiin teknisen taivutusteorian mukaiseen analyyttiseen ratkaisuun. Staattisten testien tulokset tässä työssä kehitetyllä kuorielementillä vastasivat hyvin kaupallisella elementtimenetelmällä saatuja tuloksia. Deformaatioiden ollessa geometrisesti lineaarisella alueella, kehitetyllä kuorielementillä saadut tulokset vastasivat paremmin sekä analyyttistä ratkaisua että kaupallisella elementtimenetelmällä saatuja tuloksia kuin aiemman kontinuumimekaniikkaan perustuvan kuorielementin tulokset. Kehitetyn kuorielementin ongelmana verrattuna kontinuumimekaniikkaan perustuvaan elementtiin on monimutkaisempi kinematiikan kuvaus. Tästä on seurauksena laskenta-ajan huomattava kasvaminen. Jatkossa kannattaisi keskittyä numeeristen ratkaisumenetelmien kehittämiseen.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

New insight in the relationship between regional patterns of knee cartilage thickness, osteoarthritis disease severity, and gait mechanics.

To test if the relationship between knee kinetics during walking and regional patterns of cartilage thickness is influenced by disease severity we tested the following hypotheses in a cross-sectional study of medial compartment osteoarthritis (OA) subjects: (1) the peak knee flexion (KFM) and adduction moments (KAM) during walking are associated with regional cartilage thickness and medial-to-lateral cartilage thickness ratios, and (2) the associations between knee moments and cartilage thickness data are dependent on disease severity. Seventy individuals with medial compartment knee OA were studied. Gait analysis was used to determine the knee moments and cartilage thickness was measured from magnetic resonance imaging. Multiple linear regression analyses tested for associations between cartilage thickness and knee kinetics. Medial cartilage thickness and medial-to-lateral cartilage thickness ratios were lower in subjects with greater KAM for specific regions of the femoral condyle and tibial plateau with no associations for KFM in patients of all disease severities. When separated by severity, the association between KAM and cartilage thickness was found only in patients with more severe OA, and KFM was significantly associated with cartilage thickness only for the less severe OA subjects for specific tibial plateau regions. The results support the idea that the KAM is larger in patients with more severe disease and the KFM has greater influence early in the disease process, which may lessen as pain increases with disease severity. Each component influences different regions of cartilage. Thus the relative contributions of both KAM and KFM should be considered when evaluating gait mechanics and the influence of any intervention for knee OA.

Linear-quadratic optimal control of descriptor systems

In recent years the analysis and synthesis of (mechanical) control systems in descriptor form has been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution deals with linear mechanical descriptor systems and its control design with respect to a quadratic performance criterion. Here, the notion of properness plays an important role whether the standard Riccati approach can be applied as usual or not. Properness and non-properness distinguish between the cases if the descriptor system is exclusively governed by the control input or by its higher-order time-derivatives additionally. In the unusual case of non-proper systems a quite different problem of optimal control design has to be considered. Both cases will be solved completely.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Respiratory mechanics and morphometric changes during anesthesia with ketamine in normal rats

Ketamine is believed to reduce airway and pulmonary tissue resistance. The aim of the present study was to determine the effects of ketamine on the resistive, elastic and viscoelastic/inhomogeneous mechanical properties of the respiratory system, lungs and chest wall, and to relate the mechanical data to findings from histological lung analysis in normal animals. Fifteen adult male Wistar rats were assigned randomly to two groups: control (N = 7) and ketamine (N = 8). All animals were sedated (diazepam, 5 mg, ip) and anesthetized with pentobarbital sodium (20 mg/kg, ip) or ketamine (30 mg/kg, ip). The rats were paralyzed and ventilated mechanically. Ketamine increased lung viscoelastic/inhomogeneous pressure (26%) compared to the control group. Dynamic and static elastances were similar in both groups, but the difference was greater in the ketamine than in the control group. Lung morphometry demonstrated dilation of alveolar ducts and increased areas of alveolar collapse in the ketamine group. In conclusion, ketamine did not act at the airway level but acted at the lung periphery increasing mechanical inhomogeneities possibly resulting from dilation of distal airways and alveolar collapse.

Analysis of fracture healing in osteopenic bone caused by disuse: experimental study

Osteoporosis has become a serious global public health issue. Hence, osteoporotic fracture healing has been investigated in several previous studies because there is still controversy over the effect osteoporosis has on the healing process. The current study aimed to analyze two different periods of bone healing in normal and osteopenic rats. Sixty, 7-week-old female Wistar rats were randomly divided into four groups: unrestricted and immobilized for 2 weeks after osteotomy (OU2), suspended and immobilized for 2 weeks after osteotomy (OS2), unrestricted and immobilized for 6 weeks after osteotomy (OU6), and suspended and immobilized for 6 weeks after osteotomy (OS6). Osteotomy was performed in the middle third of the right tibia 21 days after tail suspension, when the osteopenic condition was already set. The fractured limb was then immobilized by orthosis. Tibias were collected 2 and 6 weeks after osteotomy, and were analyzed by bone densitometry, mechanical testing, and histomorphometry. Bone mineral density values from bony calluses were significantly lower in the 2-week post-osteotomy groups compared with the 6-week post-osteotomy groups (multivariate general linear model analysis, P<0.000). Similarly, the mechanical properties showed that animals had stronger bones 6 weeks after osteotomy compared with 2 weeks after osteotomy (multivariate general linear model analysis, P<0.000). Histomorphometry indicated gradual bone healing. Results showed that osteopenia did not influence the bone healing process, and that time was an independent determinant factor regardless of whether the fracture was osteopenic. This suggests that the body is able to compensate for the negative effects of suspension.

Ultrasonic measurement of the elastic constants of selected nonlinear optical /semiorganic crystals with orthorhombic symmetry

Ultrasonic is a good tool to investigate the elastic properties of crystals. It enables one to determine all the elastic constants, Poisson’s ratios, volume compressibility and bulk modulus of crystals from velocity measurements. It also enables one to demonstrate the anisotropy of elastic properties by plotting sections of the surfaces of phase velocity, slowness, group velocity, Young’s modulus and linear compressibility along the a-b, b-c and a-c planes. They also help one to understand more about phonon amplification and help to interpret various phenomena associated with ultrasonic wave propagation, thermal conductivity, phonon transport etc. Study of nonlinear optical crystals is very important from an application point of view. Hundreds of new NLO materials are synthesized to meet the requirements for various applications. Inorganic, organic and organometallic or semiorganic classes of compounds have been studied for several reasons. Semiorganic compounds have some advantages over their inorganic and inorganic counterparts with regard to their mechanical properties. High damage resistance, high melting point, good transparency and non-hygroscopy are some of the basic requirements for a material to be suitable for device fabrication. New NLO materials are being synthesized and investigation of the mechanical and elastic properties of these crystals is very important to test the suitability of these materials for technological applications

Anisotropy in elastic properties of lithium sodium sulphate hexahydrate single crystal—An ultrasonic study

The double sulfate family (ABSO4), where A and B are alkali metal cations, is the object of great interest owing to the complexity and richness of its sequence of phase transition induced by temperature variation. A new sulfate salt characterized by the presence of water molecule in the unit cell with the chemical formula, Li2Na3(SO4)2⋅6H2O (LSSW), was obtained. The ultrasonic velocity measurement was done with pulse echo overlap technique [PEO]. All the six second order elastic stiffness constants, C11 = C22, C33, C44 = C55, C12, C14 and C13 = C23 are reported for the first time. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the polar plots of phase velocity, slowness, Young’s modulus and linear compressibility in a–b and a–c planes.

Elastic constant measurements of super ionic LiKSO4:Na single crystals

Elastic properties of sodium doped Lithium potassium sulphate, LiK0.9Na0.1SO4, crystal has been studied by ultrasonic Pulse Echo Overlap [PEO] technique and are reported for the first time. The controversy regarding the type of crystal found while growth is performed at 35 °C with equimolar fraction of Li2SO4H2O, K2SO4 and Na2SO4 has been resolved by studying the elastic properties. The importance of this crystal is that it exhibits pyroelectric, ferroelectric and electro optic properties. It is simultaneously ferroelastic and superionic. The elastic properties of LiK0.9Na0.1SO4 crystal are well studied by measuring ultrasonic velocity in the crystal in certain specified crystallographic directions and evaluating the elastic stiffness constants, compliance constants and Poisson’s ratios. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the surface plots of phase velocity, slowness and linear compressibility in a-b and a-c planes.

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non- linear optical coefficients,often one to two orders of magnitude higher than those of the well known inorganic non-linear optical materials.Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique using N,N-dimethyl formamide as the solvent.All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique.The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness,Young's modulus and linear compressibility surfaces along symmetry planes.The volume compressibility, bulk modulus and relevant Poisson's ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.

Comment on "Reappraisal of experimental values of third-order elastic constants of some cubic semiconductors and metals"

In a recent paper A. S. Johal and D. J. Dunstan [Phys. Rev. B 73, 024106 (2006)] have applied multivariate linear regression analysis to the published data of the change in ultrasonic velocity with applied stress. The aim is to obtain the best estimates for the third-order elastic constants in cubic materials. From such an analysis they conclude that uniaxial stress data on metals turns out to be nearly useless by itself. The purpose of this comment is to point out that by a proper analysis of uniaxial stress data it is possible to obtain reliable values of third-order elastic constants in cubic metals and alloys. Cu-based shape memory alloys are used as an illustrative example.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.