Resultant Force Vector Research Articles

Relationship Between Resultant Force Vector Acting on Human Organs From Food Bolus and the Bolus Configuration During Swallowing Using Numerical Swallowing Simulation With Moving Particle SimulationMethod.

This study investigates the forces exerted on organs during swallowing, specifically focusing on identifying forces other than those resulting from direct organ contact. Using a swallowing simulator based on the moving particle method, we simulated the swallowing process of healthy individuals upon the ingestion of thickened foods, which were simulated as shear-thinning flow without yield stress. We extracted the resultant force vectors acting on the organs and shape of the bolus at each time interval. The simulation results confirmed that the bolus originates from tongue movement and is transferred between the oral cavity and pharynx, with each organ's coordinated movements with the tongue occurring at their respective positions, as indicated by the balance of the resultant force vectors. Utilizing the information about the resultant force vectors obtained through simulations, we calculated the physical parameters of impulse, energy, and power. The variations in these physical parameters were aligned with the behaviors of both the biological system and the food bolus during swallowing. The force values calculated from the simulations closely approximate the theoretical values. Furthermore, the forces calculated from the simulations were relatively smaller than the force values derived from pressure information, such as that from high-resolution manometry and tongue pressure sensors. This difference can be attributed to the simulations extracting only the forces exerted on the organ by the food bolus. Force information on organs has the potential to provide a new interpretation of conventional mechanical indicators such as manometry and tongue pressure sensors.

Pengaruh Sudut Terhadap Besar Resultan Gaya Vektor: Kajian Eksperimental Menggunakan Praktikum Cookbook Laboratory

Vectors are fundamental concepts in mathematics and physics that play a crucial role in various scientific and engineering applications. This study investigates the relationship between the angle and magnitude of the resultant force vector using the Cookbook Laboratory practical approach. The experiment involved combining two forces at different angles and measuring the resultant force. The results indicate a linear relationship between the angle and magnitude of the resultant force, suggesting that as the angle increases, the magnitude of the resultant force also increases. However, this finding contradicts the theoretical prediction of an inverse relationship. This discrepancy is attributed to experimental limitations, particularly parallax error, which may have affected the accuracy of the measurements. Further experiments are recommended to minimize parallax error and obtain more accurate results. A thorough understanding of vector concepts and measurement techniques is essential for comprehending the relationship between angle and resultant force magnitude. Keywords: Angle; Cookbook Laboratory; Resultant Force; Vector.

Uncertainty analysis method for the output force vector control on the rib of the orienter in coiled tubing drilling

This work addresses the uncertainty associated with downhole parameters in coiled tubing drilling and proposes a new method for controlling the output force vector on the ribs of the orienter, enabling more precise control of the actual wellbore trajectory. Based on the principles of longitudinal and transverse bending beams, we construct a 3D mechanical model of the Bottom Hole Assembly (BHA) used in coiled tubing drilling. We then analyze the spatial geometry relating the force direction on the orienter's rib and the tool face angle, establishing a comprehensive steering resultant force vector model. Applying the principle of minimum energy, we explore traditional control schemes for the output force on each rib and reveal its intricate variation patterns. We conduct a statistical analysis to investigate the randomness distribution state and sensitivity of the experimental parameters, allowing us to derive the probability density and cumulative probability functions for the two-dimensional random variables linked to the output force on the ribs. Confidence interval models are constructed to predict the output forces with a predetermined level of certainty. Finally, we experimentally verify the proposed uncertainty control method in real-world coiled tubing drilling. Our results show that the randomness of weight on bit (WOB) and the tool face angle of rib 1# are the main factors influencing the uncertainty of the output force control. When the output forces vector on the ribs exceeds the uncertainty confidence interval, the actual wellbore trajectory significantly deviates from the designed one. Conversely, when the output forces vector falls within the confidence interval, the error between the actual and designed wellbore trajectories is significantly smaller. This validates the rationality and effectiveness of the proposed uncertainty analysis method, providing valuable guidance for implementing wellbore trajectory control in coiled tubing drilling.

Three-dimensional evaluation of the transverse rotator cuff muscle's resultant force angle in relation to scapulohumeral subluxation and glenoid vault morphology in nonpathological shoulders

Static posterior subluxation of the humeral head (SPSH) results in glenohumeral osteoarthritis. Treatment strategies for SPSH with or without resulting osteoarthritis remain challenging. There is growing interest in evaluating the rotator cuff muscle volume, fatty infiltration, or forces in osteoarthritic shoulders with SPSH, mainly due to a possible transverse force imbalance. In nonpathological shoulders, the transverse angle of the rotator cuff muscle's resultant force may be associated with scapulohumeral alignment and glenoid vault morphology, despite an assumed transverse force balance. The purpose of this study was to assess the transverse rotator cuff muscle's resultant force angle (TRFA) and its relationship with the scapulohumeral subluxation index (SHSI) and selected glenoid vault parameters using computer modeling. Computed tomography scans of 55 trauma patients (age 31±13years, 36 males) with nonpathological shoulders were analyzed and all measurements performed in 3-dimension. We placed landmarks manually to determine the humeral head center and the rotator cuff tendon footprints. The contours of the rotator cuff muscle cross-sectional areas were automatically predicted in a plane perpendicular to the scapula. Each rotator cuff muscle was divided into virtual vector fibers with homogeneous density. The resultant force vector direction for each muscle, corresponding to the rotator cuff action line, was calculated by vectorially summing the normalized fiber vectors for each muscle, weighted by the muscle trophic ratio. The resultant force vector was projected on the axial plane, and its angle with the mediolateral scapular axis was used to determine TRFA. The SHSI according to Walch, glenoid version angle (GVA), glenoid anteroposterior offset angle (GOA), glenoid depth, glenoid width, and glenoid radius were also evaluated. The mean values for TRFA, SHSI, GVA, GOA, glenoid depth, glenoid width, and glenoid radius were 7.4±4.5°, 54.3±4.8%, -4.1±4.4°, 5.1±10.8°, 3.3±0.6mm, 20±2mm, and 33.6±4.6mm, respectively. The TRFA correlated strongly with SHSI (R=0.731, P<.001) and GVA (R=0.716, P<.001) and moderately with GOA (R=0.663, P<.001). The SHSI was strongly negatively correlated with GVA (R=-0.813, P<.001) and moderately with GOA (R=-0.552, P<.001). The GVA correlated strongly with GOA (R=0.768, P<.001). In contrast, TRFA, SHSI, GVA, and GOA did not correlate with glenoid depth, width, or radius. Despite an assumed balance in the transverse volume of the rotator cuff muscles in nonpathological shoulders, variations exist regarding the transverse resultant force depending on the SHSI, GVA, and GOA. In healthy/nonosteoarthritic shoulders, an increased glenoid retroversion is associated with a decreased anterior glenoid offset.

Clinical Significance of the Static and Dynamic Q-angle.

Q-angle represents the resultant force vector of the quadriceps and patellar tendons acting on the patella. An increased Q-angle has been considered a risk factor for many disorders and injuries. This literature review challenges the clinical value of static Q-angle and recommends a more dynamic movement evaluation for making clinical decisions. Although there are many articles about static Q-angle, few have assessed the value of dynamic Q-angle. We searched Scopus and PubMed (until September 2021) to identify and summarize English-language articles evaluating static and dynamic Q-angle, including articles for dynamic knee valgus (DKV) and frontal plane projection angle. We also used textbooks and articles from references to related articles. Although static Q-angle measurement is used systematically in clinical practice for critical clinical decisions, its interpretation and clinical translation present fundamental and intractable limitations. To date, it is acceptable that mechanisms that cause patellofemoral pain and athletic injuries have a stronger correlation with dynamic loading conditions. Dynamic Q-angle has the following three dynamic elements: frontal plane (hip adduction, knee abduction), transverse plane (hip internal rotation and tibia external rotation), and patella behavior. Measuring one out of three elements (frontal plane) illustrates only one-third of this concept. Static Q-angle lacks biomechanical meaning and utility for dynamic activities. Although DKV is accompanied by hip and tibia rotation, it remains a frontal plane measurement, which provides no information about the transverse plane and patella movement. However, given the acceptable reliability and the better differentiation capability, DKV assessment is recommended in clinical practice.

Dynamic Analysis of an Enhanced Multi-Frequency Inertial Exciter for Industrial Vibrating Machines

Multi-frequency vibrators have advantages in bulk materials processing but their design is usually complicated. This article presents the synthesis of design parameters of a two-frequency inertial vibrator according to the specified power characteristics. Based on the developed mathematical model, the parameters of variable periodic force is derived for two angular velocities 157, 314 rad/s and their ratios 0.5 and 2. In the case of the 0.5 ratio, the instant angular velocity of the resulting force vector is 2.0–3.5 times greater than for ratio 2. A dynamical model of vibrating screen with the synthesized inertial drive is considered. It was found that at the ratio of angular velocities 0.5, the second harmonic of acceleration prevails at 50 Hz, while at the ratio of 2, the first harmonic has a greater amplitude at 25 Hz. For the first variant, the power does not depend on the initial angle between unbalances, and at the second variant, it can vary. The angle of rotation of unbalances affects the trajectory of the centre of mass and the phases of the harmonics but does not affect their amplitude. Due to such dynamical features, the two-motor inertial drive allows the vibrating machines to operate at a wider range of frequencies and amplitudes.

Coupled Aeroelastic Study of a Flexible Micro Air Vehicle-Scale Flapping Wing in Hovering Flight

Instantaneous force and structural deformation experiments were performed on a flexible, structurally characterized, low-aspect-ratio representative flapping wing. A six-component force balance was used to measure aerodynamic-force time history over a flap cycle. A VICON motion capture setup tracked the wing deformations while flapping. Measured aerodynamic forces and wing deformations were compared against coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) aeroelastic analysis results. The CFD solver is an unsteady Reynolds-averaged Navier–Stokes solver. The CSD solver is a general-purpose multibody dynamics solver capable of modeling geometrically nonlinear beam and shell elements. The CFD/CSD results were able to capture the overall trend in aerodynamic forces and wing deformations. Although predicted and measured variations in lift were similar, the drag-force magnitudes tended to be underpredicted by the coupled aeroelastic solver. The coupled CFD/CSD solver was used to evaluate the influence of wing flexibility on wing performance. Results showed that, in particular instances, decreasing wing stiffness increased the time-averaged aerodynamic lift and lift-to-power ratio. Decreased wing stiffness led to reduced leading-edge vortex circulation strength. This suggests that the increased wing performance is mainly due to a redirection of the resultant force vector allowed by the increased wing compliance.

Prediction of Anaerobic Power From Standing Long Jump in NCAA Division IA Football Players.

Mann, JB, Bird, M, Signorile, JF, Brechue, WF, and Mayhew, JL. Prediction of anaerobic power from standing long jump in NCAA Division IA football players. J Strength Cond Res 35(6): 1542-1546, 2021-Despite the popularity of the standing long jump (SLJ), limited research has explored the estimation of power developed during this test. The purpose of this study was to determine SLJ power from jump distance and selected anthropometric measures in NCAA Division IA football players. Height (Ht), body mass (Wt), thigh length, and lower leg length (LL) were measured in 58 players, allowing calculation of leg ratios of thigh length·Ht-1, LL·Ht-1, and TL·SL-1. Players performed 2-3 maximal familiarization trials of SLJ followed by 2 maximal jumps from a 3-dimension force plate sampling at 1,000 Hz. Standing long jump distance (intraclass correlation coefficient [ICC] = 0.944) and power (ICC = 0.926) calculated from resultant force and velocity vectors were highly reliable. Standing Ht (r = 0.40), Wt (r = 0.36), lower leg length (r = 0.43), total leg length (thigh + LLs) (r = 0.38), and best SLJ (r = 0.52) were significantly related (p < 0.05) to peak power, but none accounted for more than 27% of the common variance. Step-wise multiple regression identified SLJ and body mass as the only significant variables necessary to predict peak power (Power [W] = 32.49·SLJ [cm] + 39.69·Wt [kg] - 7,608, R = 0.86, SEE = 488 W, CV% = 9.3%). Standing long jump contributed 56.8% to the known variance, whereas Wt contributed 43.2%. Thus, a combination of SLJ and Wt can be used to effectively estimate explosive power in Division IA college football players.

Open GL–Open CL Solar Radiation Pressure Modeling with Time-Varying Spacecraft Geometries

A method for the fast computation of spacecraft force and torque due to solar radiation pressure (SRP) is presented. A faceted model is employed that tracks which elements of a time-varying geometry are exposed to the sunlight, but sunlight reflections are not modeled. The method uses the highly parallel execution capabilities of commodity graphics processing unit (GPU) and the Open Graphics Library (OpenGL) and Open Compute Language (OpenCL) to render a spacecraft mesh on the GPU. A custom-developed OpenGL render pipeline computes the per-model facet SRP forces and torques that are summed on the GPU before the resultant spacecraft force and torque vectors are copied back to the CPU bound process. The process is validated on spherical and cubic test shapes. The evaluation accommodates spacecraft self-shadowing and is capable of accounting for arbitrary spacecraft articulation. Material properties are encoded with the model to provide realistic specular, diffuse, and absorption surface light interactions. Numerical simulations illustrate the impact of geometric fidelity and articulated surfaces. The faceted OpenGL-OpenCL method is up to an order of magnitude faster on integrated GPU hardware than high-end graphics card as the process is not demanding on the GPU and benefits from the fast memory transfer of on-chip processors.

Mechanical and structural peculiarities of tibia shaft nonunion and its influence for treatment

Objective. To study internal tensions in bone and soft tissues of shin at normal condition and at isolated tibia nonunion, the range of fragments displacement, callous structure and to sustain the conception of treatment. Methods. Due to finite element method we created three models: I — anatomic norm; II — transverse defect of 5 mm height on the middle-lower 1/3 border filled with collagen, III — as the second model with empty fibula defect of 10 mm height on the same level 2/3–1/3 border. In 45 patients with tibia shaft nonunion (term 4–18 months) we made resection of fibula fragment 10–15 mm on the same level of tibia nonunion with apparatus of external fixation. We studied the linear bone fragments displacement and callous structure. Results. At the axial loading in normal condition (I model) there was asymmetry of tensions in the lower part of shin bones on the lateral and medial sides. At the II model vertical tensions in the lower part of tibia decreased on the medial side up to 69 % and on the lateral side — up to 44 %, tensions increased in 5 times on the lateral side of fibula. The tangential stresses increased 3 times, their resulting force vector changed the outward direction and increased 7 times. In the III model tension distribution on the tibia surface became close to normal situation. In case of tibia nonunion there was fibrous-cartilages tissues, appeared because of transverse tensions. Patients walked with weight bearing from the first days after surgery, in 95.6 % bone fragments consolidation happened in 3.5–4 months. Conclusion. Excluding of fibula from bearing function due to its 10–15 mm resection on the level of nonunion will normalize the vector of loading in the tibia fragments and fibrous-cartilage regenerate and leads to it ossification.

Intraoperative assembly of anatomical shoulder prosthesis frequently results in malalignment of the modular taper junction.

Anatomical shoulder arthroplasties (ASA) may fail because of micromotion at the modular taper junction causing wear due to fretting. Sufficient taper strength can reduce micromotion and potential reasons for failure. However, there are no normative standards for a safe assembly process performed intraoperatively by the surgeon. The purpose of this study is to determine the effect of common intraoperative assembly strategies and to identify critical influencing factors on taper stability. ASA with standard and stemless humeral component in combination with concentric Al2 O3 heads and eccentric CoCr28Mo6 alloyed humeral heads were tested. Taper angles and surface roughness were determined. Force magnitudes and impact directions were recorded using a sensorized head impactor and a three-dimensional force measuring platform. Subsequently, the axial pull-off forces were measured and taper engagement areas were macroscopically evaluated. In comparison to standard stem tapers that were impacted with an assembly device, stemless tapers were impacted into the artificial bone with significantly lower forces. Taper strength correlates to maximum impact force and was higher for CoCr28Mo6 heads with a mean pull-off ratio of 0.56 than for Al2 O3 heads with 0.37. Interestingly, all tapers showed an asymmetric clamping behavior, due to tilting during impaction. This is caused by the variation of the resulting force vector and further promoted by humeral head eccentricity. Assembly technique markedly influences the force magnitude, impact direction, impulse, and consequently taper strength. The resulting force vector and head eccentricity were identified as potential risk factors for taper malalignment.

Моделювання сходження сипкого матеріалу з відцентрового конусного дискового дозатора

Aim. Development of an analytical model and study of particle movement on the surface of a conical disk rotary dispenser-mixer of bulk material. Method. The particle, which is placed on the conical disk, is subjected to gravity directed vertically downwards, the pressure force of the vertical component of the bulk component. The force of the normal reaction of the surface of the conical disk is directed perpendicular to the cone generating line of the dispenser disk at a given point where the material particle is located. Cartesian coordinate system. The x-axis is directed along the generator line from the vertex, the y-axis is perpendicular to the x-axis and z-axis and is directed towards the rotation of the disk, and the z-axis is directed vertically upwards. The centrifugal force vector is directed along the radius. The Coriolis force is directed tangentially perpendicular to the x-axis in the opposite direction to the direction of rotation of the disk. The friction force, as the resulting force vector, is directed in the opposite direction from the direction of movement of the particle on the disk due to the centrifugal force. The force of friction of the particle on the surface of the disk decomposes into normal and radial projections. Considering an elementary particle as a material point, the differential equation of motion in vector form. Projecting the vector equality on the X and Y axis, we obtain a system of differential equations of particle motion. The numerical Runge-Kutta solution using the rkfixed function in the MathCad environment was used to solve the differential equations. Results. The speed and trajectory of the particles of bulk material depends on the angle of the conical disk and the frequency of its rotation. As the angle of the cone generating line increases, the duration of movement of the particle on the surface of the cone and the distance of movement decreases. The smoothness of movement is determined by the angle between the velocity vectors vx and vy. Smooth change of the direction of the vector of the resulting speed makes it possible to increase the accuracy of dosing the material and increases the discreteness. Scientific novelty. For the first time, a system of differential equations of motion of a material particle on a conical dispenser of centrifugal type was obtained, which takes into account the distribution of particle friction forces on the disk surface on normal and radial projections and their solution by the Runge-Kutta numerical method. Practical value. The application of the obtained system of differential equations and the algorithm of their solution makes it possible to model the design and technological parameters of the disk conical centrifugal dispenser of bulk materials.

The Effect of Varied Positioning of Mini-screw, Anterior Retraction Hook, and Resultant Force Vector on Efficient En-Masse Retraction Using Finite Element Method: A Systematic Review

Objective: The objective of this systematic review was to assess the available evidence to evaluate the effectiveness of en-masse retraction design with mini-screw with respect to the retraction hook and mini-implant position and height. Methods: The following electronic databases were searched till July 31, 2020: Pro-Quest Dissertation Abstracts and Thesis database Cochrane Central Register of Controlled Trials (CENTRAL), PubMed, Google Scholar, US National Library of Medicine, and National Research Register. En-masse retractions with anterior retraction hooks assisted by mini-implant three-dimensional finite element method (3D FEM) models were included in the study. The selected studies were assessed for the risk of bias using the Cochrane Collaboration risk of bias tool. The “traffic plot” and “weighted plot” risk of bias distribution were designed using the ROBVIS tool. The authors extracted and analyzed the data. Results: Twelve studies fulfilled the inclusion criteria. The risks of biases were low for 9 studies and high for 3 studies. Data on mini-implant, retraction hook, and the center of resistance/force vectors were extracted. The outcomes of the included studies were heterogeneous. Conclusions: According to the currently available literature review for successful bodily en-masse tooth movement, the force vector should pass through the center of resistance, which can be achieved by the clinical judgment of placing a mini-screw and an anterior retraction hook. The force from an implant placed at a higher level from the anterior retraction hook will cause intrusion; an implant placed at the medium level shows bodily movement; and an implant placed at a lower level shows tipping forces in consolidated arches.

Study of the effect of the occlusal surface of a natural tooth and fixed partial dentures supported by dental implants on the stress distribution by finite element analysis

To study the effect of the occlusal surface of a natural tooth, cement-retained and screw-retained fixed partial dentures supported by dental implants and the coefficient of friction on the stress distribution in the peri-implant bone at maximum and minimum principal stresses. Study of maximum and minimum principal stresses in models with natural teeth and artificial crowns supported by dental implants, taking into account the coefficient of friction using the finite element analysis. In models represented by fixed partial dentures supported by dental implants and a natural tooth, the maximum tensile stresses arise in the cortical bone in the cervical region of the artificial crown, and the maximum compressive stresses occur both in the cortical layer in the cervical region of the artificial crown and in the cervical region of the tooth. In models with two fixed partial dentures supported by dental implants or two natural teeth, the stress distributions in the cortical layers in the upper and lower jaw are almost identical. Modeling the antagonist and adding to the FEA model is important in order to determine the precise and realistic direction of the resulting force vector. Amplification of the number of contact areas should be considered when modeling the occlusal surface of artificial crowns supported by dental implants.

A Radial Two-Sector Gas Bearing with Maximum Load Capacity

A variational problem for a radial gas journal bearing with two sectors is considered. The pressure field in the gas layer can be described by the nonlinear Reynolds equation for arbitrary compressibility numbers. The magnitude of the resultant pressure force vector is used as a functional of the variational problem. The system of necessary conditions of the extremum is qualitatively analyzed and, as a result, a computational procedure is constructed. Based on the analysis of the complete system of necessary conditions, it is shown that the profile on each of the sectors is piecewise linear and single-stage; at the same time, one sector provides only gas rarefaction, while the other provides only gas compression.

Acoustic scattering and forces on an arbitrarily sized fluid sphere by a general acoustic field

In this work, we present a solution to the acoustic scattering problem by a fluidic sphere. The method is based on multipole expansion coefficients for a general acoustic field, which is applied to two common acoustic fields: stationary waves and arbitrarily located Bessel beams of orders m = 0 and m = 1. We present a new solution for the acoustic radiation force in terms of pressure and velocity instead of velocity potentials that are in agreement with these formulations. The behavior of the acoustic force and scattering is in agreement to the Rayleigh, Mie–like and Geometric scattering regimes. Results for force in the stationary pressure waves, typical for acoustic levitation trap, show nodes where small particles can be trapped by a restoring acoustic force. For the acoustic Bessel beam considered, the resulting force vectors point towards the corresponding intensity rings.

ROD MODELING OF STRUCTURES LEVERING MECHANISMS WITH DISTRIBUTED INERTIA

To reduce inertia of moving links into resultant force and moment vectors and to represent center of mass as node in finite element models are widely-used in mechanical calculations of linkage mechanisms. Considering distributed inertia of motion makes possible to create more precise finite element models in spatial linkage structures. By algebraically summing all the distributed inertial loads acting in both directions, perpendicular and along the axis of a constant cross section link, we can show that their intensity varies linearly along the length of link. Using this approach together with Chasles theorem for a point of free rigid body in projections onto the moving axes in the finite element method for rectilinear homogeneous rod, we reach to a more precise finite element model considering analytically distributed inertia of motion. Besides, we obtained subvectors in matrix relation which binds the generalized reaction forces acting at the contact points of the rod element with nodal generalized elastic movements. These subvectors includes the weight and inertia of a distributed spatial movement of link.

A simple improvement of a tip loss model for actuator disc simulations

AbstractThe loading of a wind turbine decreases towards the blade tip because of the velocities induced by the tip vortex. This tip loss effect has to be taken into account when performing actuator disc simulations, where the single blades of the turbine are not modeled. A widely used method applies a factor on the axial and tangential loading of the turbine. This factor decreases when approaching the blade tip. It has been shown that the factor should be different for the axial and tangential loading of the turbine to model the rotation of the resulting force vector at the airfoil sections caused by the induced velocity. The present article contains the derivation of a simple correction for the tangential load factor that takes this rotation into account. The correction does not need any additional curve fitting but just depends on the local airfoil characteristics and angle of attack. Actuator disc computations with the modified tip loss correction show improved agreement with results from actuator line, free wake lifting line, and blade element momentum simulations.

Material Configurational Forces applied to mixed-mode fatigue crack propagation and life prediction in elastic-plastic material

Within the framework of material configurational mechanics, an innovative fatigue model based on configurational force is proposed to predict the mixed-mode fatigue crack propagation in elastic-plastic material. This fatigue mode can provide the estimation of crack initiation, crack deflection, and residual fatigue lifetime simultaneously. The configurational-force fatigue model has the following basic stipulations: (a) the onset of crack growth occurs when the resultant of configurational forces reaches a critical value; (b) the crack growth takes place along the direction of resultant configurational force vector; and (c) the growth rate of mixed-mode fatigue crack is correlated to the equivalent range of material configurational forces. In order to validate the accuracy of the newly proposed fatigue model, a series of experiments are constructed by the compact tension shear specimen. The mixed-mode fatigue crack growth path and rate are obtained under different mixed-mode loading conditions. In addition, numerical implementation of configurational-force fatigue model is performed in elastic-plastic material. The results show that the mixed-model fatigue crack deflections predicted by the configurational-force fatigue model are in good agreement with experimental observations. Meanwhile the fatigue crack growth rate in elastic-plastic material has the power law relation with the equivalent range of material configurational forces, which is regardless of mixed-mode loading. It is demonstrated that the configurational-force fatigue model is able to provide a more convenient and accurate procedure to predict the mixed mode elastic-plastic fatigue crack propagation and lifetime.

The Design of Resultant Force Vector Teaching AIDS For Senior High School Students

This study aims to create the design of resultant force vector teaching aids to improve students' conceptual understandings. The method of this study is the experimental method with Pretest-Posttest Control Group Design. The sample of this study is the tenth grade of 3 natural science class (X IPA 3) as the experimental class and the tenth grade of 4 natural science class (X IPA 4) as the control class at 1 Subah Senior High School. The vector teaching aids were tested for the validity by the validator using a questionnaire. The students' responses were measured using a questionnaire. The students' concept understandings were measured from the results of the pretest and posttest scores. The result of the teaching aids' feasibility test is 98.61%, showing that the teaching aids are very feasible to use. The increase of students' concept understandings measured by the students' learning outcomes in the experimental class after using the resultant force vector teaching aids is 0.7 included in the high category. The attitude and interest responses of the students after using the teaching aids get an average percentage of 71.06% included in the high category. Based on the research results, it is recommended for the teachers to utilize the environment to create real learning