Rigid Body Spring Model Research Articles

Experimental and analytical studies on earthquake resisting behaviour of confined concrete block masonry structures

To improve the seismic performance of masonry structures, confined masonry that improves the seismic resistance of masonry structures by the confining effect of surrounding bond beams and tie columns is constructed. This study investigated the earthquake resisting behaviour of confined masonry structures that are being studied and constructed in China. The structural system consists of unreinforced block masonry walls with surrounding reinforced concrete bond beams and tie columns. The characteristics of the structure include: (1) damage to blocks is reduced and brittle failure is avoided by the comparatively lower strength of the joint mortar than that of the blocks, (2) the masonry walls and surrounding reinforced concrete bond beams and tie columns are securely jointed by the shear keys of the tie columns. In this study, wall specimens made of concrete blocks were tested under a cyclic lateral load and simulated by a rigid body spring model that models non-linear behaviour by rigid bodies and boundary springs. The results of studies outline the resisting mechanism, indicating that a rigid body spring model is considered appropriate for analysing this type of structure. Copyright © 2006 John Wiley & Sons, Ltd.

The relationship between temporomandibular joint disc morphology and stress angulation in skeletal Class III patients

The aim of this study was to examine the relationship between disc position and stress direction on the condyle by means of stress analysis using the rigid body spring model (RBSM) theory. The material consisted of 88 joints of 44 Class III dentofacial deformity patients, divided into symmetry and asymmetry groups on the basis of the Mx-Md midline position. The asymmetry group was identified by comparison with a reference midline vertical plane passing through a plane from ANS to Me. Asymmetry was diagnosed when the angle between these two planes was greater than 3 degrees. The geometry of the stress analysis model was based on sagittal tomography of the subject. The first molar, gonial angle, and the most anterior, superior, and posterior points on the condyle were plotted on a computer display, and stress angulation on the condyles was calculated with the RBSM program. In addition to anterior displacement with or without reduction, three types of disc position could be identified using magnetic resonance imaging (MRI): anterior, fully covered and posterior. In the asymmetric group, stress angulation was significantly higher (P < 0.05) at the deviation side compared with the non-deviation side. There was also a significant correlation between disc position and stress angulation (P < 0.05). In the asymmetry group, regression analysis indicated a significant correlation (P < 0.001) between the difference in stress angulation (between the deviation side and the non-deviation side) and the degree of asymmetry (measured by the angle of asymmetry). This study demonstrated that temporomandibular joint (TMJ) stress was associated with TMJ morphology in Class III patients whether or not they were asymmetric.

Mesoscopic Simulation of Failure of Mortar and Concrete by 3D RBSM

Concrete is a heterogeneous material consisting of mortar and aggregate at the meso scale. Evaluation of the fracture process at this scale is useful to clarify the material characteristic of concrete. The authors have conducted meso scale analysis of concrete over a past few years by Rigid Body Spring Model (RBSM). In this study, three-dimensional analyses of mortar and concrete are carried out, which is necessary for the quantitative evaluation of concrete behavior especially in compression. Constitutive models at the meso scale are developed for the 3D RBSM analysis. Failure behaviors and strengths in compression and tension of mortar and concrete are predicted well by the analysis. In biaxial compression test of concrete, crack in normal direction to plane of specimen is simulated that cannot be presented by two-dimensional analysis.

Experimental and Computational Modeling of Joint and Ligament Mechanics

Quantitative data on the mechanics of diarthrodial joints and the function of ligaments are needed to better understand injury mechanisms, improve surgical procedures, and develop improved rehabilitation protocols. Therefore, experimental and computational approaches have been developed to determine joint kinematics and the in-situ forces in ligaments and their replacement grafts using human cadaveric knee and shoulder joints. A robotic/universal force-moment sensor testing system is used in our research center for the evaluation of a wide variety of external loading conditions to study the function of ligaments and their replacements; it has the potential to reproduce in-vivo joint motions in a cadaver knee. Two types of computational models have also been developed: a rigid body spring model and a displacement controlled spring model. These computational models are designed to complement and enhance experimental studies so that more complex loading conditions can be examined and the stresses and strains in the soft tissues can be calculated. In the future, this combined approach will improve our understanding of these joints and soft tissues during in-vivo activities and serve as a tool to aid surgical planning and development of rehabilitation protocols.

Mesoscopic Simulation of Failure of Mortar and Concrete by 2D RBSM

Concrete is a heterogeneous material consisting of mortar and aggregate at the meso level. Evaluation of the fracture process at this level is useful to clarify the material characteristic of concrete. However, the analytical approach at this level has not yet been sufficiently investigated. In this study, two-dimensional analyses of mortar and concrete are carried out using the Rigid Body Spring Model (RBSM). For the simulation of concrete, constitutive model at the meso scale are developed. Analysis simulates well the failure behavior and the compressive and tensile strength relationship of mortar and concrete under uniaxial and biaxial stress conditions. Localized compressive failure of concrete is also simulated qualitatively.

４． 非線形力学 ＲＢＳＭ‐ＦＥＭ混合解析法による鉄筋の引抜実験解析

The paper presents a bond slip analysis between concrete and steel using the rigid body spring model (RBSM) and the finite element method (FEM) combined analysis. A new RBSM model proposed here in has 3 couples of spring normal to and parallel to the failure plane located at the center of the element with an arbitrary angle, and 4 nodes at the out side corner of the element so that this element can be installed in the FEM platform without any interface. This model can take into account the bilinear elastic plastic gap behavior and Mohr-Coulomb slip behavior including softening in elastic plastic behavior. The proposed combined model is validated by simulating Pull out test of rebar under 3 kinds of load conditions; i. e., static, high speed, impact.

A VIBRO-IMPACTING MODEL FOR THE DETECTION OF DELAMINATION

Forced oscillations of delaminated sandwich structures are dominated by impacts. A rigid body-spring model allows a discussion of the influence of internal dissipation on the system's response and the evolution of the number of impacts.

Function of digastric muscle as regards the controllability of temporomandibular joint loading: A static 2-D analysis using a rigid-body spring model

Function of digastric muscle as regards the controllability of temporomandibular joint loading: A static 2-D analysis using a rigid-body spring model

Influences of Newly Formed Woven Bone on Tissue Stresses in Rat Caudal Vertebrae Subjected to Mechanical Loading (A Study Based on Morphological Measurement Using a Micro-CT and Computational Stress Analysis).

Bone tissue stresses in mechanically loaded vertebrae were computationally investigated in order to reveal the influences of adaptive remodeling/modeling on stress distribution. Morphological alteration of the rat fifth caudal vertebrae was periodically and non-invasively measured with a microcomputed tomography (micro-CT). Von Mises stresses were calculated by using a finite element analysis (FEA) together with rigid-body spring models based on the consecutive micro-CT images. Median cross-sectional area periodically increased in the loaded rats depending on the duration of stimuli, which was caused by periosteal woven bone formation. FEA including the newly formed bone demonstrated that the loaded vertebrae showed the lower stress levels compared with non-loaded one. Averaged stress of the offset-loaded rat was markedly symmetry between ventral and dorsal sides under offset loading condition, while that of the non-loaded rat indicated asymmetry. Stress analyses suggested that the loaded vertebrae would adapt to the daily mechanical loading by depositing and calcifying woven bone over periosteum.

Force transmission through the juvenile idiopathic arthritic wrist: a novel approach using a sliding rigid body spring model

Force transmission across the wrist during a grasping maneuver of the hand was simulated for three children with juvenile idiopathic arthritis (JIA) and for one healthy age-matched child. Joint reaction forces were estimated using a series of springs between articulating bones. This method (i.e., rigid body spring modeling) has proven useful for examining loading profiles for normally aligned wrists. A novel method (i.e., sliding rigid body spring modeling) designed specifically for studying joint reaction forces of the malaligned JIA wrist is presented in this paper. Loading profiles across the wrist for the unimpaired child were similar using both spring modeling methods. However, the traditional fixed-end method failed to converge to a solution for one of the JIA subjects indicating the sliding model may be more suitable for investigating loading profiles of the malaligned wrist. The results of this study suggest that a larger proportion of force is transferred through the ulno-carpal joint of the JIA wrist than for healthy subjects, with a less than normal proportion of force transferred through the radio-carpal joint. In addition, the ulnar directed forces along the shear axis defined in this study were greater for all three JIA children compared to values for the healthy child. These observations are what were hypothesized for an individual with JIA of the wrist.

K-0338 FEMとBEMの軸対称結合モデルと接触問題への適用(G01-5 解析法)(G01 計算力学部門一般講演)

A combined model of FEM and BEM is proposed by using the concept of the Rigid-Body Spring Model. The new model is formulated for axisymmetric problems and applied to the elastic contact problems. The numerical examples show that the simple boundary elements proposed here are effective for contact problems.

THEORETICAL STRESS ANALYSIS IN WRIST JOINT – NEUTRAL POSITION AND FUNCTIONAL POSITION

A three-dimensional rigid body spring model (3D-RBSM) was used to analyse force distribution through the wrist joint. In the neutral position, 48% of the force was transmitted through the radioscaphoid fossa, 40% through the radiolunate fossa, and 12% through the triangular fibrocartilage complex. In the functional position, the wrist joint was slightly extended, resulting in significantly increased force through the lunate (53%). The lunate appears to bear more load than has been reported previously.

Functions of masseter and temporalis muscles in the control of temporomandibular joint loading--a static analysis using a two-dimensional rigid-body spring model.

Masticatory forces or bite forces applied to the teeth are known to generate a compressive force on the temporomandibular joint (TMJ). This intra-articular force is referred to as TMJ loading. TMJ loading is considered to be controlled to a certain extent by the stomatognathic system, so as not to exceed a certain limit. In order to clarify the control mechanism of the TMJ during biting, the controllability of TMJ loading through coordinated activities of the masticatory muscles has been numerically analyzed using a static two-dimensional jaw model. This model consists of a rigid-body model of the jaws and a spring model of the articular disk, which includes three dominant muscle force vectors representing the masseter, temporalis and lateral pterygoid muscles. The bite force vector is assumed to be applied solely at the first molar. Static equilibrium analyses suggest that coordinated activities of the masseter muscle and anterior portion of the temporalis muscle can minimize TMJ loading and concentrate the stress within the articular disk to the intermediate zone of the disk, and that the activity of the posterior portion of the temporalis muscle has the possibility of reducing TMJ loading.

Force transmission through the wrist joint in Kienböck's disease: A two-dimensional theoretical study

This study quantifies the changes in force and pressure distributions across the wrist joint in different stages of Kienböck's disease using a 2-dimensional computer simulation model. Twenty-four cases classified as Lichtman's stage II, IIIA, or IIIB (8 cases in each category) were analyzed using the rigid body spring model technique. A 2-dimensional model in the posteroanterior plane of the wrist was loaded through the metacarpals under a total force of 142 N. The joint forces, peak pressures, and ligament tensions calculated on the involved side were normalized against the contralateral normal side values of the same patient. The results demonstrated that significant changes of the force transmission across the wrist joint occurred only from stage IIIA to IIIB, in which scaphoid rotation was prominent. On the basis of this study, scaphoid rotation plays an important role in affecting the wrist joint contact pressure distribution. This may be responsible for the progression of Kienböck's disease.

Biomechanical Analysis of the Stress Force on Midcarpal Joint in Kienböck's Disease

Two types of lunate were recognized in the midcarpal joint. Type I lunate has no facet articulation with the hamate, and Type II lunate has a facet articulation with the hamate. The purposes of this study are to estimate the biomechanical contribution of Type II lunate for Kienböck's disease, and to elucidate the change of the contact surface between the lunate and hamate during radial and ulnar deviation for both Type I and Type II. Twenty-four contralateral unaffected wrists with Kienböck's disease were used for the first purpose. The radiographic force analysis was performed with a modified two-dimensional rigid-body spring model computer-simulation technique. Six wrists of volunteers (3 of Type I and 3 of Type II lunates) were used for the second purpose. Dynamic examination on lunohamate joint was carried out using magnetic resonance imaging. The force distribution between the radius and Type II lunate was greater than that between the radius and Type I lunate statistically. Furthermore, the impingement of articular cartilages between Type II lunate and hamate was observed in ulnar deviation on dynamic study. These results suggest that Type II lunate was one of the anatomical risk factors for Kienböck's disease.

A comparison of different methods in predicting static pressure distribution in articulating joints

Pressure distribution along the contact surface of an articulating joint model was analyzed using different numerical and analytical methods: a discrete rigid element method [rigid-body-spring-model (RBSM)], the finite element method (FEM), a simplified elasticity solution (SES) and the modified Hertzian (MH) theory. The FEM and MH methods modeled joints interposed with elastic layers, while the RBSM and SES methods assumed a simplified joint with a rigid convex indenter on an elastic concave surface. Results for an axisymmetric joint model indicate that all of these methods predict similar presure distributions on joint surfaces. In non-axisymmetric deformation mode, the RBSM method and FEM calculation showed good agreement in contact pressure prediction. Compared to the other three methods, the RBSM is relatively simple and effective in predicting joint contact pressure under symmetric and non-symmetric loading. The computational efficiency of the RBSM method is particularly attractive for pre-operative planning of reconstructive surgical procedures in orthopaedics in which geometric changes dictate the eventual outcome of the surgery.

A Combined Model of FEM and BEM and its Application to Contact Problems.

A combined model of FEM and BEM is proposed and formulated for plane stress problems using the same concept in the rigid-body spring model (RBSM). The proposed simple bond elements are applied to the problem of uniaxial tension of a rectangular plate with a circular hole which contains a circular disk with the same initial diameter as the hole. The plate is divided into boundary elements in the BEM and the disk into finite elements in the FEM. The simple bond elements are introduced into the plate-disk interface. The normal stresses on the contact arcs are compared with those determined using an exact elastic analysis and the FEM. The combined model proposed here is found to be effective for contact problems. The contact problem of a cantilever with a built-in wall is also analyzed by this method, and the elasto plastic behavior of the cantilever is analyzed.

A computer simulation study of normal and abnormal hip joint contact pressure.

The contact pressure on 112 normal hip joints and 66 acetabular dysplastic hip joints was analysed using a three-dimensional rigid body spring model. Geometric models were made from conventional anteroposterior radiographs, with the assumption that the acetabular surface was spherical. In normal hips, the distribution of contact pressure was almost even over the joint surface, and the maximum contact pressure was relatively low. However, in a dysplastic hip joint, the pressure was concentrated on the anterolateral edge of the acetabulum and increased enormously not only with the reduction in lateral coverage but also with the reduction in the anterior coverage of the acetabulum. This result indicates that a three-dimensional analysis is indispensable for estimating the mechanical effect on acetabular cartilage.

新しい剛体バネモデル・アルゴリズムによる股関節関節接触圧分布の解析

The algorithm of rigid body spring models (RBSM) is improved by adding an iteration process, with loading muscle force representing the external force, like a load incremant model.Using such an algorithm, muscle force can be input into computer analyses of human joint mechanics. This methood also means that the center of the femoral head does not need to be assumed. Moreover, changes in pressure distribution do not occur abductor muscle spring constant. This new method may be useful in evaluating muscular systems.

Determent Effect of Anchor Works Constructed in Landslide by Using Discrete Analysis

This paper discussed some problems in regard to the design of anchor work constructed in landslide. Discrete analysis of RBSM (Rigid Bodies spring Model) was used for the evaluation on mechanical effect of anchor arranged in simple slope models. The obtained basic information was as follows.The whole mass movement along the slip surface is prevented by anchor, however partial failure in interior zone of mass occurs by the increase of external force. Forms of partial failure are different depending on the difference of anchor location. The most suitable anchor location exists in the viewpoint of partial failure.The anchor stress analyzed by RBSM is lower than the calculated one by using present design equation based on Fellenius method for anchor work. The difference of both originates from the following reason. The former method evaluates the equilibrium conditions of internal force between each slice, though the latter doesn't. The most suitable anchor location decided from the view point of stress is not always same one from Partial failure.