Prediction Of Stiffness Research Articles

Design Prediction of Stiffness for Bearing Support Structure Using Rubber Components

Design Prediction of Stiffness for Bearing Support Structure Using Rubber Components

Strength and stiffness prediction models of expansive clays blended with sawdust ash

Strength and stiffness characteristics are major concern for selecting any geomaterial. However, laboratory testing of these characteristics is time associated, laborious, and high cost. So, there is a need of intelligence tools to estimate the strength and stiffness of geomaterial. The impact of sawdust ash on the stiffness and strength properties of combined expanding clays is discussed in this research. The combined expansive clays underwent tests for California bearing ratio (CBR), unconfined compressive strength (UCS), optimal moisture content, maximum dry density, plasticity characteristics (liquid limit and plastic limit), and differential free swell (DFSI). According to test results, adding more sawdust to the blended clays improves their performance. This study also investigates the artificial neural network (ANN) model that considers six input variables to forecast the CBR and UCS of blended clays. The findings demonstrate that the ANN model performs more accurately for the CBR and UCS models. This clever method may help manage the under- or overestimation of additive dosage and reduce project costs.

植入NiTi-玄武岩混编纤维增强体的复合材料螺旋弹簧刚度预测模型

植入NiTi-玄武岩混编纤维增强体的复合材料螺旋弹簧刚度预测模型

Function-oriented defect assessment in hybrid sheet molding compound tensile specimen using surrogate models

Glass fiber (GF) Sheet Molding Compound (SMC) composites are popular lightweight materials due to their good processability. Hybrid SMCs expand the field of operation, combining the high stiffness of unidirectional carbon fibers (CF) with the economic efficiency of GF. Combinations of manufacturing deviations (delamination, varying GF content, CF misorientation) occur during the production of hybrid SMCs and impede the mechanical performance of the part. A function-oriented quality assurance instead of strict tolerances is proposed. Finite element (FE) simulations are computationally too expensive for an assessment within the cycle time. Hence, surrogate models are trained on multiple parameterized FE simulations. The surrogate models shall allow for an individual functional assessment in real-time based on integrated measurement inputs. This work focuses on the generation of parametrized FE simulations for measurement inputs and surrogate modeling. Simulations and surrogate models show acceptable deviations from tensile tests for multiple combinations of manufacturing deviations. The measurement uncertainty of the stiffness prediction is assessed for both the FE simulation and the surrogate models in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM).

Performance of timber board models for prediction of local bending stiffness and strength - with application on Douglas fir sawn timber

Efficient utilization of structural timber requires accurate methods for machine strength grading. One of the most accurate methods presented this far is based on data of local fiber orientation on board surfaces, obtained from laser scanning. In this paper, two potential improvements of this method are examined. The first one consists of replacing a model based on simple integration over cross sections of boards for calculation of local bending stiffness by a 3D solid finite element (FE) model from which local bending stiffness is derived. The second improvement concerns replacement of a simple model for the fiber orientation in the interior of board by a more advanced one taking location of pith and growth direction of knots into account. Application of the alternative models on a sample of more than 200 Douglas fir boards, size 40 mm X 100 mm X 3000 mm, cut from large logs, show that each of the evaluated model improvements contributes to improved grading accuracy. When local bending stiffness is calculated utilizing the herein suggested FE model in combination with the improved model of fiber orientation in the interior of boards, a coefficient of determination to bending strength as high as 0.76 is obtained. For comparison, a coefficient of determination of 0.71 is obtain using the simpler original models.

An experimental and numerical study of brace-type long double C-section steel slit dampers

In this research study, a novel double C-section steel slit damper (DCSSD) was proposed. Six cyclic loading tests of DCSSD specimens were carried out to study the effects of strip aspect ratio, thickness of flange, damper length and steel grades on the hysteretic behaviour and resistance of the DCSSD. Test results showed that the proposed DCSSD exhibited good structural performance in terms of initial stiffness, resistance, ductility and energy dissipation capability. The equivalent damping ratio of all DCSSD specimens exceeded 0.45 while that of the DCSSD using Q160 was over 0.50. Moreover, the cumulative displacement of the DCSSD using Q160 could approach 1500 mm. Subsequently, numerical models of test specimens were built to further investigate load transfer mechanism of the DCSSD. Good agreement was observed between the numerical simulations and the test results. The distribution of the moment and shear over the strips were extracted from the FE database, and the effectiveness of the long DCSSD was confirmed by the even moment and shear distribution profile. Finally, the accuracy of the available design equations of slit steel damper (SSD) documented in the literatures for predicting the initial stiffness and resistance of DCSSD was evaluated. In general, the design models produced inconsistent predictions of the initial stiffness of the test specimens. The existing design equations for predicting the ultimate strength of the DCSSDs were relatively conservative.

Deep CNNs as universal predictors of elasticity tensors in homogenization

In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing explicit homogenization simulations. The proposed CNN model is universal in that it accounts for various types of microstructures, for arbitrary phase fractions, non-constant and thereby very large ranges of Young’s moduli of the constituent phases (from 1 to 1000 GPa) and of their Poisson’s ratios (from 0 to 0.4). Moreover, the CNN predicts the stiffness for periodic boundary conditions (BCs) along with its upper bound through kinematically uniform BCs and its lower bound through stress uniform BCs. The triple of BCs reduces the stiffness uncertainty due to the embedding of the material volume into arbitrary adjacent host materials. Beyond, the stiffness bounds provide an indicator for the proper size of a representative volume element. The proposed universal CNN model achieves high accuracy in its predictions. The reasons for the rare outliers with larger errors are rigorously analyzed. For a real, two-phase diamond–SiC coating material the universal CNN is almost as accurate as a CNN exclusively trained for fixed elastic phase properties of that material. The speedup compared to finite element computations for homogenization is above factor 20500. The proposed CNN model hence enables fast and accurate stiffness predictions in universal analyses of heterogeneous materials in their linear elastic regime.

Theoretical Prediction of the Bending Stiffness of Reinforced Thermoplastic Pipes Using a Homogenization Method

Theoretical Prediction of the Bending Stiffness of Reinforced Thermoplastic Pipes Using a Homogenization Method

Prediction of Static Bending Properties of Eucalyptus Clones Using Stress Wave Measurements on Standing Trees, Logs and Small Clear Specimens

In this study, we used both nondestructive and destructive methods for assessing solid wood properties in six Vietnamese grown Eucalyptus clones at 6 years after planting. We measured stress wave velocity in standing sample trees (SWVT), logs (SWVL), and small clear specimens (SWVS) obtained from the trees and logs, and to measure static properties, we used MOE—modulus of elasticity and MOR—modulus of rupture. The highest average MOE and MOR were detected in clones 3 and 5, suggesting that these clones might be more appropriate for breeding programs focused on improving wood quality of Eucalyptus grown in Vietnam. Mean MOE and MOR of the lumber had significant (p < 0.001) relationships with SWVT (r = 0.61 and 0.53, respectively) and SWVL (r = 0.76 and 0.71, respectively). Stress wave velocity measurements of both standing trees and logs can be useful for further segregating Vietnam’s Eucalyptus timber resource based on MOE and MOR. For the small clear specimens, the best prediction of stiffness (dynamic modulus of elasticity (MOEd)) was obtained when both SWVS and air-dry density (AD) were used. The coefficient of correlation between MOE and MOEd was 0.93.

Minimum stiffness criterion for ring frames of stringer frame stiffened shell structures

Stringer frame stiffened shell structures have been able to establish themselves as primary structures of aerospace applications because of their high ratio of load carrying capacity to weight. Unfortunately, this advantage goes hand in hand with a high level of complexity in the design of such structures. This is due to the many design variables and the complex physical behaviour caused by the interaction of stringer, frame and shell. Despite the many research activities carried out, the behaviour of such a structure under axial compression is not fully understood yet and reliable methods for an efficient calculation are lacking. In particular, the state-of-the-art sizing of frames is still based on an empirical method established in the 1950s. Within this paper, new minimum stiffness criteria are developed for the sizing of frame stiffener of stringer frame stiffened shell structures under axial compression. A novel but not fully reliable sizing method and a novel calculation method for the calculation of the panel instability load serve as a basis. For the derivation of a criterion, two different approaches are chosen and compared to each other. One approach incorporates the frame stiffnesses locally, whereas the other on a global level. Geometrically non-linear finite element analyses are performed to verify the proposed approach. The results reveal that the local consideration of the frame stiffness does not represent the physical behaviour of the shell sufficiently, whereas the minimum stiffness criterion, which incorporates the frame stiffness on a global level, delivers excellent predictions of the minimum frame stiffness.

Multiparametric modeling of composite materials based on non-intrusive PGD informed by multiscale analyses: Application for real-time stiffness prediction of woven composites

In this paper, a multiparametric solution of the stiffness properties of woven composites involving several microstructure parameters is performed. For this purpose, non-intrusive PGD-based methods are employed. From offline pre-computed solutions generated through a full-field multiscale modeling, the proposed method approximates the multidimensional solution as a sum of products of one-dimensional functions each depending on a single variable. The present work aims at providing an accurate approximation of this multiparametric solution with lower computational cost for dataset generation. Thus, a comparative analysis of three non-intrusive PGD formulations (SSL, s-PGD and ANOVA-PGD) is carried out. The obtained results reveal and demonstrate that the ANOVA-PGD model works well for approximating the stiffness properties over the entire parameter space, i.e., along its boundary as well as inside it, by using only few pre-computed high-fidelity solutions. Finally, a GUI application is developed to exploit this multiparametric solution by incorporating other composite weave architectures. This application could be easily used by engineers and composite designers, to deduce, in real-time, the macroscopic properties of woven composite for a given set of microstructural parameters by simply varying the cursors and without any microstructure generation and meshing nor FE computations using periodic homogenization.

Nonlinear Stiffness Characteristics and Model of Air Spring for Mattress based on Finite Element and Numerical Analysis

AbstractTo investigate the nonlinear stiffness characteristics and the model of an air spring for mattresses on arbitrary working conditions, a finite element model of an air spring is established, modified by response surface method and verified by uniaxial compression experiment on conditions of different initial inner pressure. Then the static stiffness characteristics on arbitrary working conditions are analyzed by finite element analysis in ABAQUS. In addition, the model for engineering control is established and the stiffness characteristics are analyzed by numerical method under working conditions. The results demonstrate the nonlinear stiffness of an air spring is positively correlated with the inner pressure and compression displacement. Additionally, a finite element model is established with average relative error ratio of 0.059 and 0.074 on conditions of compression by 20 and 30 mm, respectively, satisfying engineering requirement. Moreover, the stiffness model of an air spring on any working conditions is established by fitting surfacecontaining compression displacement and inner pressure at equilibrium position then calculating its partial derivative with respect to compression displacement. The present study suggests the nonlinear stiffness prediction model of an air spring is applicable to any working conditions, only requiring inner pressure at initial and equilibrium conditions.

Estimating the stiffness of kiwifruit based on the fusion of instantaneous tactile sensor data and machine learning schemes

Measuring the ripeness of fruits is one of the critical factors in achieving real-time quality control and sorting of fruit by growers and postharvest managers. However, recent tactile sensing approaches for fruit ripeness detection have suffered setbacks due to: (1) the nonlinear relationship between the sensor output and the true stiffness of fruits; and (2) the angle of contact, referred to as the inclination angle, between the sensor and the outer surface of the fruit. In this paper, we propose a non-destructive tactile sensing approach for estimating the stiffness of fruits, using kiwifruit as a case study. Our sensor configuration is based on a three-probe piezoresistive cantilever beam, allowing us to obtain relatively stable sensor outputs that are independent of the inclination angle of the fruit surface. Our stiffness estimation approach is based on the combination of instantaneous sensor outputs with 63 regression-based machine learning models comprising of neural networks, Gaussian process, support vector machines, and decision trees. For experiments, we used several kiwifruit samples at diverse ripeness levels. The extracted sensor data was used to train the learning models over a 10-fold cross-validation technique, allowing us to find the nonlinear relationships between the instantaneous sensor outputs and the ground truth stiffness of the fruit. Our pairwise statistical comparison by the Wilcoxon test at 5% significance revealed the competitive performance frontiers of our approach for stiffness prediction; the Gaussian process kernel functions and the binary trees outperformed other models at a mean squared error (MSE) of 1.0 and 2×10−23, respectively. Most neural network models achieved competitive learning performance at MSE less than 10−5 and the utmost performance being a pyramidal class of feed-forward neural architectures. The results portray the potential of achieving accurate ripeness estimation of fruit using intelligent tactile sensors with fast machine learning schemes across the supply chain.

Theoretical prediction for the torsional stiffness of reinforced thermoplastic pipes (RTPs) based on the strain energy-work equivalence of anisotropic cylinders

Torsional characteristics must be considered in the mechanical analysis of offshore pipelines. However, there is no specific theoretical model for RTPs to predict the torsional behavior due to the multilayered helically winding laminates. To address the problem, a theoretical model using the energy method is constructed, in which the governing equation is based on the strain energy-work equivalence of helically anisotropic hollow cylinders instead of homogenous structures in previous studies on unbonded flexible risers. The strain energy of RTPs is firstly obtained by the stress analysis of helically anisotropic elements, while the work is derived by the torsion-deformation relationship. It gives a concise theoretical expression of torsional stiffness of RTPs for the first time and greatly improves the computation efficiency. Another improvement is that it could consider the coexistence of the isotropic and orthotropic materials due to the symmetry of isotropic materials. To verify the proposed model, quasi-static torsion tests and numerical simulations were conducted on two RTP specimens. The proposed model could give accurate torsional stiffness predictions in both twisting directions. Besides, the stress distributions, the effect of thickness-radius ratios and fiber's winding angles were also investigated, in which the applicability of the proposed model was further discussed.

Experimental and Theoretical Study on the Prediction of Axial Stiffness of Subsea Power Cables

Subsea power cables are subjected to various external loads induced by environmental and mechanical factors during manufacturing, shipping, and installation. Therefore, the prediction of the structural strength is essential. In this study, experimental and theoretical analyses were performed to investigate the axial stiffness of subsea power cables. A uniaxial tensile test of a 6.5 m three-core AC inter-array subsea power cable was carried out using a 10 MN hydraulic actuator. In addition, the resultant force was measured as a function of displacement. The theoretical model proposed by Witz and Tan (1992) was used to numerically predict the axial stiffness of the specimen. The Newton–Raphson method was employed to solve the governing equation in the theoretical analysis. A comparison of the experimental and theoretical results for axial stiffness revealed satisfactory agreement. In addition, the predicted axial stiffness was linear notwithstanding the nonlinear geometry of the subsea power cable or the nonlinearity of the governing equation. The feasibility of both experimental and theoretical framework for predicting the axial stiffness of subsea power cables was validated. Nevertheless, the need for further numerical study using the finite element method to validate the framework is acknowledged.

Embedment and withdrawal stiffness predictions of self-tapping screws in timber

• Empirical equations for embedment and withdrawal stiffness of self-tapping screw in timber. • Non-linear regression analysis on embedment and withdrawal test data. • Embedment stiffness of screw increases with increasing insertion angle; decreases with increasing diameter. • Withdrawal stiffness of screw increases with increasing penetration length; decreases with increasing insertion angle and diameter. In the construction of modern multi-storey mass timber structures, self-tapping screws are the preferred fasteners. In order the maximize the strength and stiffness of self-tapping screw connections, the screws are often inserted into timber members at an angle other than 90 degrees to the face of the member. With this fabrication preference, both withdrawal and embedment stiffness relative to the grain angle of wood are important fastener properties that influence the performance of self-tapping screw connections. In certain timber systems that incorporate self-tapping screws, such as composite floor systems, their designs are often dictated by serviceability performance, which is dependent on connection stiffness. Models to predict the stiffness of self-tapping screw connection with inclined fasteners exists. These models require inputs of embedment stiffness and withdrawal stiffness when the screws load wood at different grain angles. To facilitate the application of these connection stiffness models, in this paper empirical equations are presented to directly predict the embedment and withdrawal stiffness of self-tapping screws. The models were derived by analyzing embedment and withdrawal test data obtained from various testing programs using non-linear regression analysis. The use of the proposed empirical equations will facilitate the use of connection stiffness models in design and reduce the need to conduct connection tests for a large number of combinations of fastener size, wood density and insertion angle.

Auto-tuning deep forest for shear stiffness prediction of headed stud connectors

The shear stiffness of headed stud connector is a critical parameter for the calculation of deflection and interfacial shear force for steel–concrete composite structure. Thus, this study presented a promising data-driven model auto-tuning Deep Forest (ATDF) to precisely predict the stud shear stiffness, where the novel Deep Forest algorithm is integrated with the Sequential Model-Based Optimization method to achieve automatic hyperparameter optimization. Six variables having causal relationships with shear stiffness were extracted via mechanism and model analysis, including the effect of weld collar that cannot be considered in existing models and subsequently constituting a database of 425 push-out tests. Then the ATDF model was trained by combining the advantages of deep learning, ensemble learning, and auto-tuning techniques. It was approved to significantly outperform representative benchmark models with R values of 0.91 and 0.87 for training and testing sets. The ATDF was subjected to attribute importance analysis, which quantified the stud diameter and concrete elastic modulus as the most significant variables for shear stiffness, with the stud elastic modulus having the minimal effect. The model uncertainty of ATDF was further evaluated, revealing that it had the lowest bias and variability than those in existing empirical or semi-empirical models. Finally, the reliability analysis was conducted and the partial factors of ATDF under specified target reliability were derived.

Prediction of In-plane Stiffness for the Cold-formed Steel Frame of the Wall Panel Structure

The purpose of this research was to study the lateral deformation behavior of cold-formed steel wall panel structures using experimental tests, finite element analysis and analytical methods to study the lateral stiffness of these structures. The wall panel structures were tested by full-scale experiments the experimental results of which were verified by a 3D-finite element model. The verification results showed a good correlation between the experimental tests and a finite element model. The single-column spring model was proposed for an elastic lateral stiffness analysis of the cold-formed steel wall panel structures that were formed by combinations of a guide cantilever beam and springs connection. The spring constants were defined by using the stiffness of the stub-chord connection and the bending stiffness of the chord. The experiments tests and finite element analysis were used to verify this single-column spring model. The comparison results showed good agreement between the analytical prediction, finite element analysis and experimental data in the case of the primary type of cold-formed wall structure. The proposed procedure was an efficient method for elastic lateral deformation analysis of cold-formed wall panel structures which can be used for such configurations.

Mechanical models for predicting the strength and stiffness of a beam-to-column adhesively-bonded connection between pultruded profiles

This paper presents two simple analytical expressions to predict the strength and stiffness of an adhesive beam-to-column connection between glass pultruded profiles (GFRP) subjected to shear and bending loads (vertical load applied at the free end of the beam). The joint configuration is characterized by a tubular column made of a commercially available hollow profile with a square cross section (90 mm × 90 mm × 8 mm) and two U-profiles (150 mm × 45 mm × 8 mm) arranged in the form of a built-up beam. The mechanical behaviour of this type of connection is governed by shear and bending stresses acting on the beam, with the latter becoming torsional stresses inside the adhesive layers and responsible for the failure of the connection.Regarding the strength prediction, a simple mechanical model based on the scheme of a single lap joint subjected to a traction force is presented. While, for the stiffness prediction, a simple formula for evaluating the adhesive layer deformability is proposed. With the latter, and by means of the Principle of the Virtual Power, the vertical displacement (corresponding to the vertical load applied) is evaluated and, consequently, the stiffness of the joint predicted.A comparison with the experimental results available in current literature has made it possible to verify the effectiveness of the proposed formulations which involve relatively few geometrical and mechanical parameters.

Modeling the tensile mechanical properties of silver birch timber boards

In this paper, the variability of tensile mechanical properties of silver birch timber is investigated and models for the prediction of tension strength and stiffness are developed. Through visual inspections and non-destructive tests, various strength and stiffness related indicators are identified. Destructive tension tests are subsequently performed for the determination of strength and stiffness. On each timber board, strains are measured at four localized regions, whereby, the stiffness of knot sections and clear wood sections are determined. Variability in strength, stiffness, density, knots, grain angle, and annual ring width are investigated along with the relationships between them. A hierarchical model is developed for the prediction of timber board stiffness and the reduction of stiffness due to knots. Models for the prediction of timber board strength and knot cluster strength are developed according to equality and inequality information of the failed specimens, by means of censored regression analysis. Results indicate suitable global and local predictions for silver birch timber, given the dynamic modulus of elasticity, median slope of grain, and knot geometries.