Putkistotukien lineaarinen mallintaminen dynaamisissa analyyseissä

Nuclear power plant piping systems exhibit dynamic behaviour, and piping supports keep the displacements of the pipes within acceptable limits. This study investigates linear modelling methods for nonlinear piping supports in dynamic analyses and presents a procedure to linearize nonlinear supports. The procedure and methods are found in literature and they were furher developed here. The study is limited to supports with gap and friction. The goal is to represent the nonlinear system as accurately as possible by an equivalent linear system. Using the linear system, computational effort can be saved in the dynamic analyses. The nonlinear supports are replaced by linear springs or spring-damper systems to obtain a linear system. The equivalent spring and damping constants are found by iterative procedure, based on selected linearization method. Several methods are presented. Once the equivalent properties have been found, the equivalent linear system is obtained. Linearization procedure was investigated using single and multiple degree-of-freedom examples. Linearization was then applied to a real-world piping system with four gap supports. For the real-world system, an equivalent linear system was determined and comparison with original nonlinear model was made for the load case investigated. The compared parameters were maximum displacements, support forces and bending moments in the pipe at the support locations. For the system studied, maximum displacements were of the same order of magnitude, though large differences occured at single locations. Maximum support forces were generally smaller in the linear system. Pipe bending moments differed significantly, and were both higher and smaller in the linear system. Linearization methods of piping supports need to be further developed, so that other types of supports can be linearized and that the equivalent linear system corresponds better to the original nonlinear system.Ydinvoimalaitosten putkistot käyttäytyvät dynaamisesti, ja putkistotuet estävät siirtymiä kasvamasta liian suuriksi. Tässä työssä tutkitaan epälineaaristen putkistotukien lineaarisia mallinnusmenetelmiä dynaamisissa analyyseissä ja esitetään menettelytapa epälineaaristen tukien linearisoimiseksi. Menettelytapa ja mallinnusmenetelmät löytyvät kirjallisuudesta ja tässä työssä niitä kehitettiin edelleen. Työ rajoittuu välys- ja kitkatukiin. Tavoitteena on kuvata epälineaarinen systeemi mahdollisimman tarkasti ekvivalentilla lineaarisella systeemillä. Lineaarisen systeemin käytöllä voidaan säästää aikaa dynaamisissa analyyseissä. Epälineaariset tuet korvataan lineaarisilla jousilla tai jousi-vaimennin systeemeillä lineaarisen systeemin saamiseksi. Ekvivalentti jousivakio ja vaimennuskerroin määritetään iteraatiomenettelyllä perustuen valittuun linearisointimenetelmään. Useita menetelmiä esitetään. Kun ekvivalentit arvot on löydetty, ekvivalentti lineaarinen systeemi on saatu. Linearisointimenettelyä tutkittiin yhden vapausasteen ja monen vapausasteen esimerkkisysteemeillä. Menettelyä sovellettiin todelliseen putkistoon, jossa oli neljä välystukea. Todelliselle putkistolle muodostettiin ekvivalentti lineaarinen systeemi, jota verrattiin alkuperäiseen epälineaariseen malliin tutkitulla kuormitustapauksella. Tukien kohdalla verrattiin maksimisiirtymiä, tukien voimia ja putken taivutusmomenttia. Tutkitulle systeemille maksimisiirtymät olivat samaa suuruusluokkaa, mutta suuria eroja esiintyy yksittäisissä paikoissa. Tukien maksimivoimat ovat yleensä pienempiä lineaarisessa systeemissä. Putken taivutusmomentit eroavat merkittävästi ja ovat sekä suurempia että pienempiä lineaarisessa systeemissä. Putkistotukien linearisointimenetelmiä on tarpeen jatkokehittää siten, että myös muunlaisia tukia voidaan linearisoida ja että ekvivalentti lineaarinen systeemi vastaisi paremmin alkuperäistä epälineaarista systeemiä

Near infrared spectroscopic evaluation of biochemical and crimp properties of knee joint ligaments and patellar tendon

Knee ligaments and tendons play an important role in stabilizing and controlling the motions of the knee. Injuries to the ligaments can lead to abnormal mechanical loading of the other supporting tissues (e.g., cartilage and meniscus) and even osteoarthritis. While the condition of knee ligaments can be examined during arthroscopic repair procedures, the arthroscopic evaluation suffers from subjectivity and poor repeatability. Near infrared spectroscopy (NIRS) is capable of non-destructively quantifying the composition and structure of collagen-rich connective tissues, such as articular cartilage and meniscus. Despite the similarities, NIRS-based evaluation of ligament composition has not been previously attempted. In this study, ligaments and patellar tendon of ten bovine stifle joints were measured with NIRS, followed by chemical and histological reference analysis. The relationship between the reference properties of the tissue and NIR spectra was investigated using partial least squares regression. NIRS was found to be sensitive towards the water (R2CV = .65) and collagen (R2CV = .57) contents, while elastin, proteoglycans, and the internal crimp structure remained undetectable. As collagen largely determines the mechanical response of ligaments, we conclude that NIRS demonstrates potential for quantitative evaluation of knee ligaments.publishedVersionPeer reviewe

Estimating mechanical properties of bovine knee ligaments and tendons with near infrared spectroscopy

In this study, mechanical properties of bovine knee ligament and tendon samples were estimated using near infrared spectroscopy (NIRS). Properties related to sample stress-relaxation characteristics were found to be suitable for NIRS-based estimation

Near infrared spectroscopic evaluation of ligament and tendon biomechanical properties

Knee ligaments and tendons are collagen-rich viscoelastic connective tissues that provide vital mechanical stabilization and support to the knee joint. Deterioration of ligaments has an adverse effect on the health of the knee and can eventually lead to ligament rupture and osteoarthritis. In this study, the feasibility of near infrared spectroscopy (NIRS) was, for the first time, tested for evaluation of ligament and tendon mechanical properties by performing measurements on bovine stifle joint ligament (N = 40) and patellar tendon (N = 10) samples. The mechanical properties of the samples were determined using a uniaxial tensile testing protocol. Partial least squares regression models were then developed to determine if morphological, viscoelastic, and quasi-static properties of the samples could be predicted from the NIR spectra. Best performance of NIRS in predicting mechanical properties was observed for toughness at yield point (median QCV2=0.54, median normalized RMSE = 6.1 %), toughness at failure point (median QCV2=0.53, median normalized RMSE = 6.6 %), and the ultimate strength of the ligament/tendon (median QCV2=0.52, median normalized RMSE = 8.3 %). Thus, we show that NIRS is capable of estimating ligament and tendon biomechanical properties, especially in parameters related to tissue failure. We believe this method could substantially enhance the currently limited arthroscopic evaluation of ligaments and tendons

Physiological and degenerative loading of bovine intervertebral disc in a bioreactor: A finite element study of complex motions

Intervertebral disc (IVD) degeneration and regenerative therapies are commonly studied in organ-culture experiments with uniaxial compressive loading. Recently, in our laboratory, we established a bioreactor system capable of applying loads in six degrees-of-freedom (DOF) to bovine IVDs, which replicates more closely the complex multi-axial loading of the IVD in vivo. However, the magnitudes of loading that are physiological (able to maintain cell viability) or mechanically degenerative are unknown for load cases combining several DOFs. This study aimed to establish physiological and degenerative levels of maximum principal strains and stresses in the bovine IVD tissue and to investigate how they are achieved under complex load cases related to common daily activities. The physiological and degenerative levels of maximum principal strains and stresses were determined via finite element (FE) analysis of bovine IVD subjected to experimentally established physiological and degenerative compressive loading protocols. Then, complex load cases, such as a combination of compression + flexion + torsion, were applied on the FE-model with increasing magnitudes of loading to discover when physiological and degenerative tissue strains and stresses were reached. When applying 0.1 MPa of compression and ±2–3° of flexion and ±1–2° of torsion the investigated mechanical parameters remained at physiological levels, but with ±6–8° of flexion in combination with ±2–4° of torsion, the stresses in the outer annulus fibrosus (OAF) exceeded degenerative levels. In the case of compression + flexion + torsion, the mechanical degeneration likely initiates at the OAF when loading magnitudes are high enough. The physiological and degenerative magnitudes can be used as guidelines for bioreactor experiments with bovine IVDs.ISSN:1751-6161ISSN:1878-018