Incremental-iterative Method Research Articles

A novel iterative algorithm for nonlinear inelastic dynamic analysis of truss structures; MCB-Spline+Sp time integration method

The focus of this work is on the development of a novel algorithm for the nonlinear dynamic analysis of structures. In the sake of a general and easy-to-implement solution method, the tangential stiffness matrix is calculated by combining the Cauchy-Riemann equations derived from the differentiation of complex functions and using the nodal displacement perturbation vector. An implicit direct time integration method based on a cubic B-Spline is integrated with the incremental-iterative method using a quadrature rule based on the interpolation of spline functions, which is referred to as the MCB-Spline+Sp time integration method. A step-by-step algorithm for developing a computer code to implement this method is provided. The effectiveness of the proposed approach is evaluated through several nonlinear time history analyses, which demonstrate its accuracy and efficiency by observing less computational efforts and fast convergence rate. Moreover, a comparison is made between the developed method and well-established techniques such as the Newmark and Standard-Bathe time integration methods in combination with the iterative Newton-Raphson method.

Enhancing the Functionality of Management Internship and Community Service Through Maintenance Of Web Application

Universities play a crucial role in developing high-quality human resources through Internship and Community Service Programs, which prepare students with professional skills and relevant competencies. However, implementing these programs often faces issues such as inefficiencies in registration, documentation, and progress reporting. To address these challenges, a university department developed and implemented a comprehensive web-based application system. This research aims to improve and refine the application through software maintenance processes, employing an iterative incremental method with phases including planning, requirements, analysis and design, implementation, testing, and evaluation, conducted repeatedly according to the prioritized order of feature improvements. After being maintained, the application is tested through functional testing using black box techniques and automation tools. Results indicate that the maintenance process successfully ensured the application functions according to established scenarios and requirements, thereby enhancing support for administrative processes of internships and community service programs and overcomes previous management challenges.

Mixed node's residual descent method for hyperelastic problem analysis

Geometric nonlinearities, material nonlinearities, and volume locking are the notable challenges faced in hyperelastic analysis. Traditional methods in this regard are complex and laborious for implementation as they require linearization and formulation of global matrix equations while simultaneously addressing volumetric locking. A mixed node's residual descent method (NRDM) proposed herein can effectively address the numerical challenges associated with geometric nonlinearities, material nonlinearities, force nonlinearities, and incompressibility. First, the implementation of the NRDM is considerably simplified as unlike traditional incremental–iterative methods, it's a matrix-free iterative method that does not require incremental linear equations. Second, the NRDM addresses the geometric and material nonlinearities with relative ease as it flexibly describes the deformation with the initial configuration or assumed deformed configuration as the reference frame. Third, the NRDM prevents the occurrence of volumetric locking by employing hydrostatic pressure as an independent variable. Furthermore, the NRDM can easily treat the force nonlinearities and boundary nonlinearities by controlling the relation between load and deformation during iteration. Moreover, a notable accuracy of the NRDM is confirmed through numerical verifications, and several critical matters are discussed, including the scheme for adjusting the basic independent variables, treatment of displacement boundaries, scheme for imposing loads, and computational parameter setting.

Load-end shortening curve of stiffener elements with beam-column buckling considering steel grades based on empirical formulae of critical stress

The existing load-end shortening formulae with beam-column buckling in CSR-H were derived from the theoretical buckling formulae of stiffener elements considering the effective width of attached plate. However, due to different yielding stress and plastic flow ability, the critical stress of stiffener elements for elastic-plastic beam-column buckling may be relevant to steel grades. The critical stress of beam-column buckling was analysed by numerical method and compression test under supply supported constraints. Separate seven steel column samples from slender to sturdy were designed to be studied for various grades of steel mainly including 921A, S355 and Q235. After comparison, the empirical formulae of critical stress considering different yield stress were proposed in power exponent expression, and then employed to replace the theoretical buckling formulae in the load-end shortening curves in incremental-iterative method. This new load-end shortening expression of stiffener elements with beam-column buckling mode could more accurately evaluate the progressive collapse behaviours under longitudinal compression.

A numerical algorithm for gas foil bearing simulation with considering three-dimensional structure

This paper presents a coupled algorithm for gas foil bearing simulation with considering three-dimensional structure. In the discretization process of the top foil, the plate and shell elements are compared to evaluate their advantages in terms of computational time and deviation. Based on the displacement constraints, the bump foil is simplified as a series of separated bumps and their interaction forces are calculated by the penalty function method. To solve the nonlinearity of the foil deflection caused by the frictional contact, the incremental iteration method is introduced in the simulation. The calculation accuracy of the proposed algorithm is verified by the experimental results and its efficiency is superior to the existing methods.

Ultimate strength of aged ships under hull structure’s imperfections

Ship hull structures, particularly those with extended service life, contain various imperfections, including initial deformities, residual stresses, and corrosion-induced degradation. Such variables critically influence the structural integrity of the hull girder. Consequently, comprehending the residual strength capacity of the hull girder is paramount for guaranteeing the vessel’s operational safety and dependability, especially under severe loading scenarios. The existing methods to determine the hull girder’s ultimate bending moment either ignore imperfections or consider imperfections such as initial deformations or residual stresses but with the assumption of a fixed level. In the current study, the stress distribution method and incremental-iterative method are used; and solutions are proposed to cover factors such as initial deformations, residual stresses, and corrosion. A single skin bulk carrier, 56,000 DWT of deadweight, is employed as the demonstrative example. Eleven cases of imperfections are suggested, and the variations of ultimate bending moment for hogging and sagging conditions under the effect of uncertainties are analyzed and evaluated. The results of the current study are offered and discussed. Several concluding remarks are also presented.

The convergence of a generalized convex neural network

ABSTRACT The convergence of neural networks is a central area of research that is essential in understanding the universal approximation capability and the structural complexity of these systems. In this study, we investigate a generalized convex incremental iteration method. This iteration method is presented in a more general form than previous studies and is capable of scraping a broader range of weight parameters. Additionally, we systematically demonstrate the convergence rate of the convex iteration. Our findings are also easily extensible to deep convolutional neural networks, which helps to explain their effectiveness in various real-world applications. Furthermore, we provide a discrete statistical perspective to address issues of input data non-compactness and unknowability of the objective function in practical settings. To support our conclusions, we propose two algorithms, namely back propagation and random search, the latter of which can prevent the network from getting stuck in a local minimum during training. Finally, we present results from several regression problems, which indicate that our algorithms exhibit superior performance and are consistent with our theoretical predictions. These results provide a more comprehensive understanding of the convergence of neural networks and its significance in the universal approximation capability of these systems.

Auto-balancing bridge based wide impedance spectrum measurement with consideration of Op-Amp input impedance.

In an auto-balancing bridge for high impedance measurements, an operational amplifier (Op-Amp) is used to follow the intermediate potential. However, the input impedance of the Op-Amp introduces significant effects in high impedance measurements. This paper proposes a two-step excitation method (TSEM) and an incremental iterative method (IIM). The TSEM determines the magnitude of the Op-Amp input impedance and the initial value of the device under test. The IIM utilizes the TSEM results as initial conditions to quickly bring the bridge to equilibrium. To overcome the distortion issues associated with small amplitude excitation signals generated by the DAC under low resolution conditions, a programmable gain amplifier is designed. Additionally, a half-cycle difference algorithm is developed prior to the three-parameter sine fit to mitigate low-frequency direct-current drift caused by power frequency, thus improving measurement accuracy. Experimental results demonstrate that when the reference impedance is set to 1 MΩ, impedance measurements ranging from 1 kΩ to 100 MΩ can be achieved within the frequency range of 1 to 100kHz. The precision evaluation reveals a relative standard deviation (RSD) of the modulus better than 0.384% and a standard deviation (SD) of the phase angle better than 3.49 mrad; especially for the impedance under test of 1 MΩ, the RSDis better than 0.006% and the SDis better than 0.1 mrad.

A Numerical Analysis Model of Composite Pneumatic Formwork Considering the Stiffness Contribution of Polyurethane Layer

Pneumatic formwork is a kind of inflated fabric-polyurethane composite formwork formed by spraying polyurethane on the interior surface of the membrane. A numerical analysis model of composite pneumatic formwork considering the stiffness contribution of polyurethane is proposed to predict the structural response. The analysis model simulates the component of fabric and polyurethane with membrane elements and shell elements respectively, and Tie constraint of surface to surface is defined at the interface. A nonlinear material model for fabric is adopted considering the influence of stress ratio and loading history, and the constitutive relation of polyurethane is described in the foaming plane with different properties for tension and compression. Newton-Raphson incremental iterative method is used to solve the involved nonlinear problems. The simulation accuracy of the proposed analysis model is verified by comparing its predictions with test results about the loaddeformation response of an inflated membrane structure and the corresponding composite pneumatic formwork under horizontal loading. The numerical model is further used to investigate the influence of the thickness of polyurethane layer on the improvement of overall structural stiffness of a larger pneumatic formwork under horizontal fresh gale, and the polyurethane is proved to be beneficial for the shape-control of pneumatic formwork.

Research on Constitutive Model and Algorithm of High-Temperature-Load Coupling Damage Based on the Zienkiewicz–Pande Yield Criterion

The mechanical properties of rock can be weakened under the influence of high temperatures. To describe the mechanical behavior of rock under the action of high temperature more accurately, based on the Zienkiewicz–Pande yield criterion, the damage variable Dc which accounts for the coupling between high temperature and load is introduced. According to plastic potential theory and plastic flow law, the iterative incremental method for a high-temperature and load-coupled damage constitutive model in Flac3D is deduced in detail and compiled into the corresponding dynamic link library file (.dll file). By modifying the shape function to degenerate into the Mohr–Coulomb constitutive model, an elastic–plastic analysis of an ideal circular tunnel is performed, and a comparison is made between calculation results obtained from the built-in Mohr–Coulomb constitutive model in Flac3D, proving the correctness of the secondary development program. Finally, numerical simulations are conducted to study the effects of high-temperature damage using rock uniaxial compression tests, and the model’s validity is established by comparing it with previous experimental results.

Three-dimensional Non-linear Finite Element Analysis of Impact Response and Damage in Laminated Composite Shells

The impact response and the impact-induced damage in curved composite laminates subjected to transverse impact by a metallic impactor are studied using three-dimensional non-linear transient dynamic finite element formulation. A layered version of isoparametric eight-noded hexahedral element with incompatible modes is developed which incorporates geometrical non-linearity based on total Langragian approach. The non-linearity of both strain displacement relation and contact loading are simultaneously solved using Newton-Raphson incrementaliterative method. Impact-induced damages (matrix cracking and delamination) are predicted using appropriate three-dimensional stress-based failure criteria. Some example problems of graphite/epoxy laminated cylindrical shells with variation of important parameters such as impactor velocity, shell curvature, laminate dimension and fibre orientation of plies are solved and the influence of geometrical non-linear effect on both impact response and resulting damages is demonstrated.

Novel incremental procedure in solving nonlinear static response of 2D-FG porous plates

The manuscript presents a nonlinear mathematical model capable to investigate the nonlinear bending response of Bi-directional functionally graded (BDFG) plate resting on elastic foundations including large deformations in the sense of von Kármán. A unified higher order shear plate theory is used to implement the shear influence with parabolic distribution through thickness direction. The gradation of materials is portrayed by power law function through axial (x-direction) and thickness (z-direction). The governing equations consist of a set of four nonlinear coupled partial differential equations. The assumption that the material properties change in the x- direction complicates the governing equations since they have variable-coefficients. Winkler–Pasternak model is exploited to present the elastic foundations with normal and shear deformations. In this work, a novel incremental–iterative method is proposed, and some tricky computational issues are performed to ensure stable and fast convergence rates even with large incremental load steps. The differential/integral quadrature method (DIQM) is developed to numerically discretize the variable-coefficient governing equations on a rectangular plate with different boundary conditions. Parametric studies are presented to illustrate the impact of nonlinear strains, gradation indices, geometrical properties, and boundary conditions on the transverse displacement, normal and shear stresses.

Hull girder ultimate strength of bulk carrier (HGUS-BC) evaluation: Structural performances subjected to true inclination conditions of stiffened panel members

To enhance the safety of ship structure design, this study evaluated time-dependent hull girder ultimate strength considering thick corrosion and the inclination conditions of stiffened panels. The hull girder ultimate strength was calculated using incremental–iterative methods based on IACS-CSR in a bulk carrier hull model. The corrosion effect was measured as the thickness reduction in structural members, and inclination conditions were considered such as non-uniform uniaxial thrust, which influences the yield strength of structural members. The corrosion effect was investigated from 5 to 20 years of service time, wherein the corrosion rate was obtained based on a reference and was then divided into standard and severe corrosion rate conditions. The effect of non-uniform uniaxial thrust was considered the yield stress reduction on all the stiffener elements in an inclined position. The safety level of the design within each timeframe of the measured corrosion effect was then considered based on the ultimate limit state. This study found that the corrosion rate greatly affects HGUS, with severe corrosion having a greater affect than standard corrosion. In 20 years of service time with uniform loads in hogging conditions, the highest HGUS reduction caused by standard corrosion is 5.87%, while severe corrosion causes a reduction of 24.48%. Moreover, non-uniform uniaxial thrust was found to have a negative effect on HGUS, lowering the HGUS value on benchmark hull models both in hogging and sagging conditions.

Pengembangan Backend Investasi Berbasis Website pada Ekosistem Digital Ihya dengan Metode Iterative Incremental

Technological developments in the industrial era 4.0 are very fast coupled with the COVID-19 pandemic. The digital ecosystem is one that has developed rapidly during the pandemic, many people need a complete platform to meet all their needs, so the presence of a digital ecosystem is expected to provide all user needs. One of the things that users want in a digital ecosystem is an investment module. The existence of a digital ecosystem with an investment module will greatly help people who need capital and creation due to the pandemic. However, at this time there are still few digital ecosystems that have this module. So there is a need for a digital ecosystem that has an investment module to make it easier for users to access and use it, so the creation of a website-based digital ecosystem called Ihya, especially on the investment module. The creation of the digital ecosystem website was made using the iterative incremental method as its development method. The development of the Ihya digital ecosystem on investment modules made using the PHP programming language with the Laravel framework and the CSS Bootstrap framework, and stored in a MySQL database. The investment module in the Ihya digital ecosystem was tested using the black-box testing, user acceptance test, and load test methods. After testing, the Ihya digital ecosystem investment website meets user needs as an investment platform with a user acceptance test value of 85.1%.

Pengembangan Back-End Ekosistem Digital Ihya Pada Modul Crowdfunding Dengan Metode Iterative Incremental

The current economic growth in Indonesia is clearly closely related to the development of the digital era which is always evolving and transforming. Technological developments have not gone unnoticed, especially the economy and the increasing number of applications during the pandemic. Poverty rates and rates of increase are also increasing. One solution in today's digital era is the digital ecosystem. Digital ecosystems can help the process of exchanging information that is integrated with each other and contains various platforms in one container. In the survey of the need for the application of a digital ecosystem, 55.3% answered the need for a digital ecosystem, and the crowdfunding platform was the most preferred choice by 59.6% of respondents. There are many generous people who have more sustenance and want to help others in need, but are afraid to donate and meet in person, so an online crowdfunding platform is needed in this digital ecosystem called Ihya. This crowdfunding platform helps donors who want to donate, as well as fundraisers who need help and want to raise money. Back-end website development using Laravel with iterative incremental method. At the end of the development of the crowdfunding website platform, testing is carried out using black-box testing, namely scenario testing, as well as load testing, and user acceptance tests. The results of the user acceptance test that get a value of 88.8% which shows the user has felt helped by the features that have been made.

Application of Equivalent Single Layer Approach for Ultimate Strength Analyses of Ship Hull Girder

The objective of this paper is to present the application of equivalent single layer (ESL) approach for the ultimate strength assessment of ship hull girder in the context of numerical finite element (FE) simulations. In the ESL approach, the stiffened panel is replaced with a single plate, which has the equivalent stiffness of the original panel. Removal of tertiary stiffening elements from the numerical model facilitates time-savings in pre-processing and FE analysis stage. The applicability of ESL approach is demonstrated with two case studies, one compartment model and full-sized double hull tanker model in intact and damaged conditions. The damage extents are determined based on the international association of classification societies from common structural rules (IACS-CSR) for oil tanker. Ship hull girder is exposed to distributed pressure with the sinusoidal shape that bends the hull girder. This pressure load is applied separately to bottom and side structures to obtain the vertical and horizontal bending moments of the hull girder, respectively. Ultimate strength predictions obtained from ESL approach are compared to full three-dimensional finite element method (3D FEM) and IACS incremental-iterative method. The comparison between different methods is provided in terms of longitudinal bending moment and cross sectional stress distribution. Overall, ESL approach yields good agreement compared to the 3D FEM results in predicting the ultimate strength of ship hull girder while providing up to 3 times computational efficiency and ease of modeling.

A Simplified Model for Numerical Investigation of Bump-Type Foil Bearings Based on Contact Nonlinearity

Abstract The paper introduces a simplified structural model for the numerical investigation of bump-type foil bearings. This analytical model is based on an efficient nonlinear contact procedure with consideration of friction, small deformations, and elasticity. The bump foil is modeled with a truss structure, while the top foil uses two-dimensional (2D) beam elements. In this present model, the normal and tangential contact forces between the bump foil and the bearing sleeve and between the foils are dealt with the penalty method. Even for a simple loading, the contact state might change between separation, stick, and slip. To avoid convergence problems caused by discontinuity, the regularized smooth friction model is used instead of the Coulomb friction model. In addition, due to contact problems that depend on time are accompanied by nonlinear evolution, the solution of the system equation using the incremental iterative method and the Newton–Raphson method is presented. The deflection of the top foil is added to the film controlled by the Reynolds equation (RE) to obtain the air pressure distribution. The theoretical predictions of the rotor push-pull tests agree well with results from the literature, which verifies the validity of the model. Using this present model, the quasi-static behaviors of the foil structure are mainly discussed, and parametric studies concerning environmental pressure and radial clearance are also conducted.

Numerical analysis of configuration for steel lazy-wave riser in deepwater

ABSTRACT The steel lazy-wave riser (SLWR) is modelled by nonlinear large-deformation beam theory. The equilibrium equations of the SLWR are established based on Minimum Total Potential Energy Principle. The numerical solution adopts an incremental iterative method, which can effectively deal with the riser-seabed interaction and avoid the complexity of contact detection. The method can be used for parameter optimisation. Firstly, introduced the overall configuration and characteristics of SLWR. Secondly, discuss the different working conditions of SLWR. Lastly, it describes how to choose a reasonable range of parameter research and determine each optimal configuration option. The method was verified with Orcaflex. Through static analysis, the effects of water depth, horizontal span, upper catenary length, extreme sea conditions, and motion of vessel on the configuration of the riser, top tension, bending moment, and shear force distribution are obtained.

A pseudo-inverse decomposition-based self-organizing modular echo state network for time series prediction

Echo state network (ESN) refers to a popular recurrent neural network with a largely and randomly generated reservoir for its rapid learning ability. However, it is difficult to design a reservoir that matches a specific task. To solve the structure design of the reservoir, a pseudo-inverse decomposition-based self-organizing modular echo state (PDSM-ESN) is proposed. PDSM-ESN is constructed by growing–pruning method, where the error and condition number are used, respectively. Since the self-organizing process may negatively affect the learning speed, the pseudo-inverse decomposition is adopted to improve learning speed, which means the output weights are learned by an iterative incremental method. Meanwhile, to solve the ill-posed problem, the modular sub-reservoirs corresponding to the high condition number are pruned. Simulation results indicate that PDSM-ESN has better prediction performance and run-time complexity compared with the traditional ESN models.

A Novel Incremental Iterative Force Recovery Method for Second-Order Beam-Column Elements in Plastic Hinge Analysis of Steel Frames

This paper is concerned with an incremental iterative force recovery method in the second-order plastic hinge analysis of steel frames mainly modelled by a single element per member. Second-order beam-column elements are preferred in the direct analysis of steel frames due to their high accuracy and efficiency. However, formulations of these elements are complicated, and therefore they may have a problem of getting element force recovery in inelastic analysis. To overcome this difficulty, a novel incremental iterative force recovery method for second-order beam-column elements is proposed to perform plastic hinge analysis. The proposed method is derived more strictly and has good performance. Also, the section assemblage approach and the refined plastic hinge method are adopted in this study to consider the gradual degradation of section stiffness in the plastic hinge analysis. To verify the accuracy, efficiency and robustness of the proposed method, several benchmark examples are analyzed by the proposed method and compared with solutions reported by early researchers.