Analysis Of Elastic Structures Research Articles

A mechanics-based data-free Problem Independent Machine Learning (PIML) model for large-scale structural analysis and design optimization

Machine learning (ML) enhanced fast structural analysis and design recently attracted considerable attention. In most related works, however, the generalization ability of the ML model and the massive cost of dataset generation are the two most criticized aspects. This work combines the advantages of the universality of the substructure method and the superior predictive ability of the operator learning architecture. Specifically, using a novel mechanics-based loss function, lightweight neural network mapping from the material distribution inside a substructure and the corresponding continuous multiscale shape function is well-trained without preparing a dataset. In this manner, a problem machine learning model (PIML) that is generally applicable for efficient linear elastic analysis and design optimization of large-scale structures with arbitrary size and various boundary conditions is proposed. Several examples validate the effectiveness of the present work on efficiency improvement and different kinds of optimization problems. This PIML model-based design and optimization framework can be extended to large-scale multiphysics problems.

Dynamic substructuring for visco-elastic materials using a POD-based model reduction method: application to laminated panels

Dynamic substructuring is now a well established and powerful tool for engineers used to analyze the dynamic response of mechanical systems. The technique is particularly favored for the simulation of mechanical vibrations allowing different aspects to be studied. It consists in splitting the global structure into several substructures from which reduced models are built. In Finite Element software, these reduced models, also called superelements, are generally built using the concept of Component Mode Synthesis. Difficulties arise when structures made of frequency-dependent materials are considered since classical modal reduction algorithms are inapplicable as they are because of the frequency-dependence of the stiffness matrix. Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. The methodology takes advantage of the Golla-Hughes-McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The coupling of the superelement with a host structure is achieved via the use of Lagrange multipliers. The reduced system takes the form of a constant matrix of very small size compared to the original FE model. The method is applied to laminated panels such as an automobile windscreen.

Three-dimensional creep calculation model for reliability analysis of concrete-filled steel tubular (CFST) structure

For long-span concrete-filled steel tube (CFST) structure, it is essential to implement efficient and realistic prediction models for the long-term processes of core concrete creep. In order to systematically study the main influential factors in CFST structure creep effects, a probabilistic analysis can be performed. The objective of this paper is to analyse the long-term response of CFST structure by using time-dependent reliability method. To address the problem of creep calculation, a novel and comprehensive presentation was developed. By converting the integral-type creep law to a differential-type form with internal variables, based on the Kelvin chain model, an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains was established. We have compiled a three-dimensional (3-D) finite-element analysis programme that considers the creep Poisson effect of core concrete to analyse the long-term performance of the CFST structure. This is achieved by developing a commercial finite element code, such as Usermat in ANSYS. As calculation examples, several time-dependent analyses of a CFST stub column and long-span CFST arch bridge were performed. The calculated results of long-term behaviour agree well with experimental and measured data. Considering the randomness of various input parameters, such as physical dimensions and materials of the CFST structure, we have analysed the uncertainty using the Latin-hypercube-sampling (LHS) stochastic finite-element method. The results of creep sensitivity analysis revealed that coefficient of creep model uncertainty, steel and concrete elastic modulus were the three most influential parameters for CFST stub columns’ creep, and load, coefficient of creep model uncertainty, relative humidity, steel and concrete elastic modulus were the five for CFST arch bridges’ long-term deflection. In addition, the use of Monte Carlo (MC) and response surface (RS) methods for structural stochastic reliability analysis demonstrates the ability of these approaches to assess the reliability index of long-span CFST arch bridges. This provides a valuable reference for the design and performance evaluation of CFST structures.

Generic and simplified approaches for the structural analysis of precast concrete sandwich panels

This paper presents a comparison between three numerical models developed for the structural analysis of composite precast concrete sandwich panels under lateral loading. The first model is based on a full finite element analysis where “slip” between the layers is obtained from the elastic deformability of the various components. The second model is based on a simplified finite element analysis where the effect of the shear connectors is smeared and modeled through an effective shear stiffness of the insulation layer. The third approach provides closed-form expressions for evaluating the deflection and is based on the classical sandwich beam theory where the shear connectors are considered through the effective stiffness of the insulation, similar to the second model. The structural response obtained from the three models was compared for various panel configurations and good correlation was obtained. A reasonable agreement with test results from the literature was also demonstrated. Therefore, both the simplified finite element model and the classical sandwich beam theory (closed-form solution) are recommended for the elastic structural analysis and for estimating the degree of composite action at the serviceability limit state of precast concrete sandwich panels.

Effects of Plastic Injection Moulding Process Parameters on Material Elastic Modulus on Complex Geometry and Parameter Optimization for Getting Maximum Stiffness

Plastic injection is widely used in white goods sector in case of highly production rates, low transformation costs and recyclability of products. There are many parameters affecting on the quality, dimensional stability and mechanical strength in plastic injection process. In washing machine tubs which are exposed to dynamic loads during spinning, it is necessary to optimize process parameters. In this research; packing pressure, packing transition point, packing time and injection time is optimized by using Box Behnken methodology via Moldlfow elastic modulus outputs and structural analyses results. Optimum process parameters are obtained to achieve best material orientation.

Seismic response of reinforced concrete buildings, considering the effective stiffness in beams, columns and structural walls

The Peruvian Technical Standard E.030 for Seismic Resistant Design allows the analysis of the elastic range of buildings, considering gross stiffness. However, Peruvian Standard E060 considers the effects of axial loads, cracked regions in structural elements, and load duration. This research focuses on the impact of incorporating effective stiffness in seismic responses (displacements, drifts, and vibration periods) for six, seven, and eight-story reinforced concrete structures. The study quantifies the increase in seismic responses for design earthquakes and suggests that using effective stiffness in elastic analyses can reduce structural damage. To analyze seismic responses, three buildings of different heights were selected, meeting drift limits established by Standard E.030 using the gross section. Subsequently, twelve structural cases and combinations were created and analyzed in the ETABS program, employing the CQC criterion allowed by Standard E030. Different combinations of effective moment of inertia values for elastic analyses, according to ACI 318 (2014), were used. The study found that the simultaneous reduction of gross inertias of columns, beams, and structural walls led to a 1.2-fold increase in period and a 1.5-fold increase in drift, with variations based on the building's height. In conclusion, it is recommended to consider effective stiffness in elastic structural analyses to minimize displacement damage and ensure better structural performance during severe seismic events.

Three-dimensional plasticity-based topology optimization with smoothed finite element analysis

AbstractThis paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures.

Static and dynamic analysis of couple-stress elastic structures by using peridynamic differential operator

In this paper, a peridynamic differential operator (PDDO) method is developed to analyze the static and dynamic responses of size-dependent elastic structures in the frame of a consistent couple stress theory (CCST). The displacement governing equations together with the boundary conditions of the couple-stress static problems are transformed from the local differential form to the nonlocal integral form through a fourth-order PDDO and then solved by a meshfree scheme. For dynamic cases, the time-domain problems are first transformed into frequency domain by Fourier transform, then solved by the PDDO meshless method in the frequency domain. The time-domain results are finally obtained by using an exponential window method (EWM). The size effects on the static and dynamic responses of some typical elastic problems are investigated by the developed PDDO method. A very high level of computational accuracy is achieved by comparing with the analytical solutions and the existing numerical results.

Dynamic substructuring for mechanical systems with frequency-dependent materials using a POD-based model reduction method

Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. Contrary to classical modal reduction techniques (Craig-Bampton, MacNeal) where the normal modes basis must be enriched to account for damping effects, the methodology presented here takes advantage of the Golla–Hughes–McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The Lagrange multipliers are finally employed to couple the reduced system to a host structure, as made in popular dynamic substructuring techniques. This method has two major advantages. First, substantial savings are achieved by the judicious combination of GHM and POD techniques. Second, the reduced system takes the form of a constant matrix of small size which permits to preserve confidentiality.

A Problem-Independent Machine Learning (PIML) enhanced substructure-based approach for large-scale structural analysis and topology optimization of linear elastic structures

Structural analysis for structures composed of highly heterogeneous materials which often involves the solution of large-scale linear algebraic equations is very time-consuming even within the linear elastic regime. Furthermore, the tremendous computational cost of iterative large-scale finite element analysis also prevents the widespread use of topology optimization as a powerful design tool especially when the desired design resolution is very high. In order to break the bottleneck hindering the efficient solutions of large-scale structural analysis and design optimization problems, in the present article, a general machine learning (ML) enhanced substructure-based framework is proposed. The essential idea is resorting to the classical substructure-based finite element analysis approach and establishing an implicit mapping between the parameters characterizing the material distribution within a substructure and the corresponding condensed stiffness matrix/numerical shape functions through offline trained deep neural networks. In contrast to most of the existing ML enhanced approaches, the proposed framework is truly independent of the forms of structural geometry, boundary condition and external load, and can be applied to solve various boundary value problems governing by the same type of partial differential equation once the offline training is completed. Armed with modern artificial intelligence techniques, the proposed approach in some sense revives the classical substructure approach in finite element analysis. Compared with the traditional paradigm, it can achieve 104–105 times solution efficiency for tested large-scale examples with satisfactory accuracy. The effectiveness of the approach was also validated for the non-adjoint topology optimization problems, i.e., 3D compliant mechanism design. Finally, to demonstrate the proposed approach’s capability in dealing with extremely large-scale three-dimensional problems, a three-dimensional topology optimization problem with about 109 design variables and 3×109 degrees of freedom (Dofs) is solved on a laptop without resorting to any parallel computing techniques.

Bifurcations and Stability Analysis of Elastic Slender Structures Using Static Discrete Elastic Rods Method

Abstract Discrete elastic rods (DER) method provides a computationally efficient means of simulating the nonlinear dynamics of one-dimensional slender structures. However, this dynamic-based framework can only provide first-order stable equilibrium configuration when combined with the dynamic relaxation method, while the unstable equilibria and potential critical points (i.e., bifurcation and fold point) cannot be obtained, which are important for understanding the bifurcation and stability landscape of slender bodies. Our approach modifies the existing DER technique from dynamic simulation to a static framework and computes eigenvalues and eigenvectors of the tangential stiffness matrix after each load incremental step for bifurcation and stability analysis. This treatment can capture both stable and unstable equilibrium modes, critical points, and trace solution curves. Three representative types of structures—beams, strips, and gridshells—are used as demonstrations to show the effectiveness of the modified numerical framework, which provides a robust tool for unveiling the bifurcation and multistable behaviors of slender structures.

Statics analysis and strength optimization of squirrel cage elastic support structure

Statics analysis and strength optimization of squirrel cage elastic support structure

Strength evaluation of support frame of the low level liquid effluent pipes of nuclear plant

Disposal of low level radioactive liquid effluents of nuclear plant into the sea is carried out through carbon steel pipes inside a guard pipe. The treated effluents are discharged inside the sea beyond breaker zone through two disposal pipes. The disposal pipe discharges the treated effluent to two numbers of 1 m diameter pipe which goes down till sea bed. This guard pipe should be supported on top of the jetty against wind, wave, and dead loads. This study is intended to cover the design adequacy and material selection of the liquid discharge piping support configuration. Material and coating requirements of the support frame is chosen after careful evaluation of the prevailing saline environment and economic consideration. Elastomeric bearing provides necessary support & firm adherence of the support arrangement to the erected pile cap. Elastomeric bearing are easy to install and offer low maintenance. The support frame is checked for dead load, pipe load, live load, wind load, wave ¤t loads, and seismic loads. Wave and current loads were calculated based on Morison semi empirical equation. Linear elastic structural analysis of the support frame was carried out. This article provides insight to the materials used in supporting this pipelines and the basis behind the material selection. After material selection, strength evaluation of the structure is elaborately carried out for all the loads. Indian standards and API recommended practice were adopted for the strength assessment of the structure. Support arrangement is formed using trusses at different levels, spandrel girders and hangers connecting the spandrel girders. All the stresses for structural arrangement for liquid discharge pipe support are checked and found within acceptable limits.

Research on the vibration characteristics of an embedded elastic metamaterial plate

For a class of embedded elastic metamaterial plate, a general vibration analysis process is given based on the idea of equivalent analysis, which combines the equivalent medium theory and the classical thin plate vibration theory. The embedded elastic metamaterial plate is treated as an equivalent homogeneous plate with abnormal effective medium parameters by using the equivalent medium theory, and then the natural vibration characteristics and steady-state vibration characteristics are investigated. The results show that the semi-analytic form of the vibration analysis process is effective, which can obtain the vibration characteristics of such heterogeneous and complex structures quickly and accurately within the medium and low frequency regions. The results also reveal the plate’s anomalous behaviors that are quite different from the traditional homogeneous plates. For the natural vibration, there exists no natural frequency in the band gap and they can be formed only in the pass band. These modes tend to gather gradually when approaching the initial frequency of the band gap, and the closer to the lower band edge of the band gap, the smaller the distance between natural frequencies and the greater the modal density. Additionally, the modes of the corresponding orders before and after the band gap are identical on the macro level but completely different on the unit-cell level. For the steady-state vibration, there is no resonance peak in the band gap, the resonance peaks are distributed denser and denser when approaching the initial frequency of the band gap, and the distribution of the displacement field at corresponding order of resonance peaks before and after the band gap is also similar on the macro level. This work not only facilitates the design and analysis of elastic metamaterial plate structures, but also deepens the understanding of their extraordinary vibration characteristics and expands the design space of mode characteristics.

Contactless modal analysis of elastic structures with acousto-elastic transmission matrix

Modal analysis is a major issue in the industry to identify resonances in mechanical parts. Indeed, resonances can induce high vibration levels that are potentially destructive. Active modal analysis methods require on the one hand to excite the controlled part and on the other hand to record the induced displacements/acceleration/stresses. Conventional methods, called SIMO, involve a mechanical excitation source associated with several receivers. More rarely, the analysis is performed with several sources and one receiver (MISO). Finally, for several years, MIMO techniques with several sources and several receivers are commonly implemented. However, for some parts, it may be difficult to implement an array of mechanical sources. That is why, here, we propose to carry out the modal analysis with a set of 8 loudspeakers as sources, and the measurements are performed at a large number of measurement points using a LASER vibrometer. The analysis of the singular value decomposition of the contactless transmission matrix allows to identify superposed modes. We will discuss the advantages and disadvantages of such a configuration. This method based on acousto-elastic coupling is successfully applied to the modal analysis of two axi-symmetric parts: a pinion and a rotating wheel. Finally, we will see that the same device can be used to control vibration fields.

Co-rotational Reduced Order Kalman Filter Finite Element Method for the Real-time Implementation of Large-scale Structural Models

The real-time implementation of large-scale structural models without sacrificing their physical realism is challenging. This paper introduces a conceptual framework named the Co-rotational Reduced Order Kalman Filter Finite Element Method (CROKF-FEM) for the realistic linear elastic analysis of large-scale structures in real-time. The standard linear finite element method (FEM) is employed for high-precision deformation modeling, and element matrices are pre-computed in the space domain. To avoid the inflated elements of standard linear FEM due to large rotation, a co-rotational formulation is devised. Then, the system is discretized in the time domain using the Wilson- θ implicit integration scheme and a further state-space model is developed. Subsequently, a reduced-order model is constructed using the balanced truncation method. Finally, a Kalman filter algorithm is created on the reduced model for online estimation. This approach preserves all the benefits of traditional linear FEM with a similar deformation accuracy while achieving significant real-time performance.

Elastic structural analysis based on graph neural network without labeled data

AbstractArtificial intelligence is gaining increasing popularity in structural analysis. However, at the structural system level, the appropriateness of data representation, the paucity of data, and the physical interpretability of results are rarely studied and remain profound challenges. To fill such gaps, a physics‐informed model named StructGNN‐E (i.e., structural analysis based on graph neural network [GNN]–elastic) based on the GNN architecture, which is capable of implementing the elastic analysis of structural systems without labeled data, is proposed in this study. The systems with structural topologies and member configurations are organized as graph data and later processed by a modified graph isomorphism network. Moreover, to avoid dependence on big data, a novel physics‐informed paradigm is proposed to incorporate mechanics into deep learning (DL), ensuring the theoretical correctness of the results. Numerical experiments and ablation studies demonstrate the unique effectiveness of StructGNN‐E against common DL models, with an average accuracy of 99% and excellent computational efficiency. Due to its differentiability, StructGNN‐E is promising for bidirectionally linking structural parameters and analysis results, paving the way for a new end‐to‐end structural optimization method in the future.

Elastic shape analysis of brain structures for predictive modeling of PTSD.

It is well-known that morphological features in the brain undergo changes due to traumatic events and associated disorders such as post-traumatic stress disorder (PTSD). However, existing approaches typically offer group-level comparisons, and there are limited predictive approaches for modeling behavioral outcomes based on brain shape features that can account for heterogeneity in PTSD, which is of paramount interest. We propose a comprehensive shape analysis framework representing brain sub-structures, such as the hippocampus, amygdala, and putamen, as parameterized surfaces and quantifying their shape differences using an elastic shape metric. Under this metric, we compute shape summaries (mean, covariance, PCA) of brain sub-structures and represent individual brain shapes by their principal scores under a shape-PCA basis. These representations are rich enough to allow visualizations of full 3D structures and help understand localized changes. In order to validate the elastic shape analysis, we use the principal components (PCs) to reconstruct the brain structures and perform further evaluation by performing a regression analysis to model PTSD and trauma severity using the brain shapes represented via PCs and in conjunction with auxiliary exposure variables. We apply our method to data from the Grady Trauma Project (GTP), where the goal is to predict clinical measures of PTSD. The framework seamlessly integrates accurate morphological features and other clinical covariates to yield superior predictive performance when modeling PTSD outcomes. Compared to vertex-wise analysis and other widely applied shape analysis methods, the elastic shape analysis approach results in considerably higher reconstruction accuracy for the brain shape and reveals significantly greater predictive power. It also helps identify local deformations in brain shapes associated with PTSD severity.

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.

Static analysis of elastic cable structures under mechanical load using discrete catenary theory

In this paper, the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory. A cable net is discretized into multiple nodes and edges in our numerical approach, which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation. A fully implicit framework is proposed based on the discrete differential geometry (DDG) theory. The equilibrium configuration of a target object is derived by adding damping force into the system, known as the dynamic relaxation method. The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation. A more intricate scenario is further discussed in detail, where a structure consisting of multiple slender cables is connected through joints. Utilizing the robustness and efficiency of our discrete numerical framework, a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers. Finally, an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties, material characteristics, component numbers, and cable orientations. Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures, and could motivate innovative designs in both mechanical and civil engineered equipment.