Nonlinear Static Structural Analysis Research Articles

Design and structural analysis of non-pneumatic tyres for different structures of polyurethane spokes

NPTs have vast applications because of no tyre puncture, no need for air pressure, low rolling resistance, and also have higher flexibility for design and recyclability. In this research work, different structures of polyurethane (PU) spokes have been designed and analyzed under radial loading conditions which include structures like honeycomb with varying cell angles, simple spoke, and trapezoid type by keeping in view that the cell wall thickness and somehow the mass of the structures remain the same. Based on the Mooney-Rivlin hyper-elastic material model and performing 2D non-linear static structural analysis on different types of NPTs using ANSYS, it has been observed that the simple spoke structure has the lowest spoke stress and deformation values of 2.01 MPa and 11.7 mm, while HC–A1 has the least value of strain energy of 2.58 mJ, at a load of 2500 N. The above results show that the straight spoke structures like simple spoke and trapezoid type have a high load-carrying ability than the honeycomb type NPTs under same boundary conditions. While honeycomb NPTs have higher fatigue life as compared to straight-spoke NPTs.

Performance evaluation of a reticulated shell with atmospheric corrosion damage

The study on damage evaluation induced by atmospheric corrosion of engineering structures has attracted more and more international concern over the past three decades. However, the effects of atmospheric corrosion on reticulated shells have not been systematically investigated. In this regard, the performance assessment of a reticulated shell subjected to atmospheric corrosion damage is actively conducted in this study. The atmospheric corrosion model of shell elements is first presented, and a refined exponential model for estimating the corrosion depth of steel materials is developed by using the pattern recognition technique. The sensitivity of stiffness matrix to element thickness is established by using Euler–Bernoulli beam element. The sensitivity of mass matrix to element thickness is developed based on lumped mass assumption. Then, the expression of natural frequency sensitivity to element thickness and mass is derived by considering the section loss induced by both the inner and outer surface corrosion. In addition, the explicit expression of frequency sensitivity to mass of spherical joints is also established in detail. The nonlinear static structural analysis is conducted to evaluate effects of atmospheric corrosion on the stress of structural elements. A real reticulated shell constructed in northern China is taken as the example structure to examine the feasibility of the proposed approach and to assess the potential damage caused by atmospheric corrosion to the structure.

Realization of reinforced concrete structures analysis with the account of physical and geometrical nonlinearity in computer program PRINS

An algorithm of physically and geometrically nonlinear static analysis of structures by the finite element method is described, the distinguishing feature of which is the use of a full nonlinear stiffness matrix. This matrix is represented as the sum of five terms, namely, the stiffness matrix of the zero, first and second order, as well as matrices of initial displacements and initial stresses. When using modified Lagrange coordinates, the matrix of the initial displacements becomes a zero matrix. The calculation is carried out by a step-by-step method. Features of the application of this technique in the calculation of reinforced concrete structures are considered. The examples of static nonlinear analysis of reinforced concrete structures with the aid of program PRINS are given.

Further Improvements in the SNUF Blade Design by Numerical Design Optimization Framework

This paper focused on improving a small-scaled helicopter rotor blade prototype with a flap-driving mechanism termed the Seoul National University Flap (SNUF). The design of the SNUF included realizing vibratory load reduction. First, a multibody structural dynamics analysis was performed to determine the influence of the flap dimension and location within the rotor blade with respect to hub vibratory load reduction. This process was followed by selecting a specific blade configuration that maximized vibration reduction capability. Following this, a numerical optimization technique was applied to improve the cross sectional design of the SNUF blade. The design optimization procedure obtained improved blade sectional design with decreased first torsional frequency and reduced blade weight, and it satisfied sufficient structural integrity. Three-dimensional nonlinear static structural analysis also was performed for the optimized SNUF design. The von Mises stress distribution on the blade and components was predicted by considering external aerodynamic loads, centrifugal loads because of rotation, and contact among the internal components. Future studies will include fabricating the prototype blade on the basis of the optimized design and performing a whirl tower test.

Modification of dynamic increase factor to assess progressive collapse potential of structures

Progressive collapse assessment of buildings against column removal requires a time consuming nonlinear dynamic analysis therefore nonlinear static analysis considering a proper dynamic increase factor (DIF) can be utilized as an alternate analysis to predict maximum dynamic response of structures. In this study, the effect of post-elastic stiffness ratio of members on DIF in nonlinear static analysis of structures against column removal is investigated, and a modified empirical DIF is presented. For this purpose, series of low and mid-rise moment frame structures with different span lengths and number of stories are analyzed. For each ratio of post elastic stiffness, a non-linear dynamic analysis and a step-by-step nonlinear static analysis are carried out. The results of analysis reveal post-elastic stiffness ratio is an efficient parameter on DIF. Therefore the new empirical formulas including moment demand, ductility and post-elastic stiffness ratio are suggested. Finally, it is shown that the proposed DIF formulas are accurate and efficient.

Dynamic Increase factor based on residual strength to assess progressive collapse

In this study, a new empirical method is presented to obtain Dynamic Increase Factor (DIF) in nonlinear static analysis of structures against sudden removal of a gravity load-bearing element. In this method, DIF is defined as a function of minimum ratio of difference between maximum moment capacity (Mu) and moment demand (Md) to plastic moment capacity (Mp) under unamplified gravity loads of elements. This function determines the residual strength of a damaged building before amplified gravity loads. For each column removal location, a nonlinear dynamic analysis and a step-by-step nonlinear static analysis are carried out and the modified empirical DIF formulas are derived, which correspond to the ratio min of beams in the bays immediately adjacent to the removed column, and at all floors above it. Therefore, the new DIF can be used with nonlinear static analysis instead of nonlinear dynamic analysis to assess the progressive collapse potential of a moment frame structure. The proposed DIF formulas can estimate the real residual strength of a structure based on critical member.

Effects of damping ratio on dynamic increase factor in progressive collapse

In this paper, the effect of damping ratio on nonlinear dynamic analysis response and dynamic increase factor (DIF) in nonlinear static analysis of structures against column removal are investigated and a modified empirical DIF is presented. To this end, series of low and mid-rise moment frame structures with different span lengths and number of storeys are designed and the effect of damping ratio in DIF is investigated, performing several nonlinear static and dynamic analyses. For each damping ratio, a nonlinear dynamic analysis and a step by step nonlinear static analysis are carried out and the modified empirical DIF formulas are derived. The results of the analysis reveal that DIF is decreased with increasing damping ratio. Finally, an empirical formula is recommended that relates to damping ratio. Therefore, the new modified DIF can be used with nonlinear static analysis instead of nonlinear dynamic analysis to assess the progressive collapse potential of moment frame buildings with different damping ratios.

Preoperative Image-Based Simulation of Carotid Artery Stenting Considering Agatston Score of Calcified Plaques

The role of calcification inside fibroatheroma during carotid artery stenting operation is controversial. Cardiologists face a major problem in placing stents: “plaque protrusion” i.e. elastic fibrous caps containing early calcifications that penetrate inside the stent. The aim of this work is to assess the contribution of calcification to plaque vulnerability by using image-based models of carotid artery stenting. Technically, Finite Element Analysis was used to simulate the balloon and stent expansion as a preoperative virtual framework. A nonlinear static structural analysis was performed on 20 image-based models of patients reconstructed from Multidetector Computer Tomography (CT) angiography acquisitions. Subject-specific local Elastic Modulus (EM) of calcified plaques was estimated using the Agatston Calcium (Ca) score, as obtained from CT images. The main findings from the personalized simulations are that maximum values of von Mises stress of 102kPa and 329kPa are obtained on calcified plaques when patient-specific balloon pressure expansion and stent self-expansion, respectively, are modeled. In modeling stent expansion procedure, it is observed a statistically significant positive correlation for EM of calcification with maximum stress (R=0.55; p=0.013) and Plaque Wall Stress (PWS) (R=0.47; p=0.038), while no significant correlation is observed for Ca score with maximum stress (R=0.28; p=0.23) and PWS (R=0.27; p=0.26), this last result suggesting a moderate impact of Ca score in plaque rupture. The approach proposed here could enrich the arsenal of tools available for pre-operative prediction of carotid artery stenting procedure in the presence of calcified plaques. Keywords: Atherosclerotic calcification, calcified plaques, carotid artery stenting, finite element analysis, plaque mechanics, subject-specific model.

Stochastic life-cycle cost analysis of wind parks

We develop a life-cycle cost model for assessing wind parks; implementing the model requires calculation of cost components that are related to wind tower structural performance for multiple wind hazard levels. We compute the structural capacity of the wind towers by means of nonlinear static structural analysis for three wind hazard levels; then, the limit state dependent and life-cycle costs for the wind park are calculated based on the proposed model. The wind load for each wind hazard level is based on actual collected data and is generated probabilistically. Application of the proposed life-cycle cost analysis model is tested for a wind park with known characteristics (number and location of wind towers, wind potential, and so on).

An energy-based approach for nonlinear static analysis of structures

Current codes and guidelines provide different methods to perform nonlinear static analysis of structures that require some non-intuitive assumptions in their application. In the present paper an energy-based method for nonlinear static analysis that allows to overcome these assumptions is proposed. In the method the capacity and the demand are both expressed in terms of energy. An energy capacity curve is computed considering that at each step the work of the lateral forces is equal to the structure internal work. The demand is represented in terms of an energy quantity, defined pseudo-energy, that is computed from both the maximum response displacement and the maximum response force. Constant ductility pseudo-energy spectra are introduced as energy demand design spectra, alternative to the input energy demand spectra. The definition of the performance point does not require iterative procedures for equating the internal dissipated energy to the demand energy. For the direct evaluation of the performance point two different operative procedures are proposed. The proposed method is evaluated comparing the earthquake-induced deformations of single degree-of-freedom systems resulting from the application of the presented nonlinear static analysis procedures with those obtained from the time-history analysis and from the application of the EC8 nonlinear static analysis procedure. The method is also applied in the case of a RC plane frame representing the inner frame of a six story building. The results obtained with the proposed method are in good agreement with those computed using nonlinear dynamic analyses, moreover they are characterized by a better accuracy with respect to the results obtained with the method provided by EC8.

Limit state analysis of reinforced shear walls

The nonlinear analysis of reinforced concrete structures is revisited. In particular, reference is made to the nonlinear static analysis of structures containing shear walls, for which we present a dedicated shell element. The developed element formulation is flexible enough to allow for nonlinear material constitutions for concrete and re-bars and arbitrarily distributed steel reinforcement. Moreover, for shear walls coexisting with frame elements within the same structural system, it allows to capture the effects of localized actions such as concentrated forces or moments transmitted by the nearby framed part the structure. Numerical results are presented that demonstrate the effectiveness of the proposed approach in finite element computations.

Probability density evolution method and its application in life-cycle civil engineering

A family of generalised probability density evolution equations (GPDEE) have been developed in recent years based on the principle of preservation of probability incorporated with uncoupled physical equations, which take advantages over classical probability density evolution equations. With the aid of the GPDEE, the time-dependent analysis of a life-cycle engineering system is further investigated. The basic probability density evolution equation for nonlinear static analysis of structures and for time-dependent analysis is presented, respectively. By these new developments, the time-dependent reliability of a life-cycle engineering system, involving deterioration of materials, degradation of components and the rehabilitation or maintenance process, could be approached in a unified framework. Numerical investigations show an effective application to a life-cycle engineering system, which also, as indicated, provides a potential tool for reliability-based or risk-based decision-making for life-cycle civil engineering in the long run.

Failure Mode Estimation with Inter-Fiber Failure Analysis of Composite Wind Turbine Blade

This paper provides an overview of the failure mode estimation result with 3D finite element (FE) analysis model of wind turbine blade. In order to predict the realistic behavior in the whole blade region, fiber failure (FF) and inter-fiber failure (IFF) analysis were applied to account delamination or matrix failure on composite materials. The Puck’s fracture criteria were used for the IFF evaluation. For the comparison of FE analysis result with the measured data of static test, a 3.5m down-scaled wind turbine blade was designed and fabricated using glass fiber epoxy composite materials. A nonlinear static structural analysis was performed and then the failure mode and the location were estimated with the FF and IFF analysis.

Theory and Experimental Study on Flexure Spring Based Fermat Curve

Flexure springs are used in linear compressors and expanders to maintain the clearance seal between the piston and cylinder.The design method of Fermat flexure spring has been put forward.The fermat flexure spring can be obtained by adjusting the space distribution of spiral arms together with the parameters of Fermat curve including base radius r,coefficient of curvature c,start angle ?,curve angle θ,etc.Then the mathematical models were set up to analyze the axial and radial stiffness of the fermat flexure.Geometrically nonlinear static structural analysis and nonlinear dynamics structural analysis which base on the finite element software(ANSYS) and the performance test is made to fermat flexure spring.The feasibility of the method to design Fermat flexure spring,the validity of the numerical analysis and finite element analysis,are proved by comparing the calculated results,simulated results and experimental results.

Finite Element Analysis of Different Flexure Springs

Flexure spring suspensions have demonstrated the ability to provide long operating lifetimes for cryocoolers. The good flexure spring need high radial stiffness and high fatigue life. The profile curves are very important for flexure spring. In this paper, based on the finite element analysis software (ANSYS), geometrically nonlinear static structural analysis and nonlinear dynamics structural analysis were made to several different flexure springs. The fatigue strength, axial and radial stiffness, modal frequency were calculated and listed. The different performance between linear flexure spring and spiral flexure spring were discussed, which would provide an advisory opinion for the design and application of flexure spring in space cryocooler.

Nonlinear Static Analysis of Structures with Rocking Columns

In simple inelastic structures subjected to severe base motions, the maximum acceleration response is bound by the yield strength and is inversely proportional to its mass. It can be demonstrated that a similar effect is approximately produced in structures with multidegrees of freedom. In strong structures, the maximum acceleration response is dependent on the intensity of the earthquake. However, if the strength of the structure is reduced, the maximum acceleration response and associated forces in its structural and nonstructural components can be substantially reduced. If some of the structural columns (carrying gravity loads) are allowed to rock, providing very small resistance to lateral loads, it is possible to reduce the strength of the global structural system and limit the global accelerations in seismic events. However, before overturning such columns may have substantial resistance which may void the effectiveness of weakening. The objective of this study is to (1) develop a simplified analytical model for rocking columns from fixity to overturning; (2) build the computational tools to simulate the behavior of structures including such rocking columns; and (3) examine the global nonlinear static response of a weakened structure. An analytical model is developed using an equivalent flexibility approach, which considers rigid body rotations and flexural deformations. Physical experiments of rocking columns were performed, and the results are used for the calibration and validation of analytical models. An analytical model of a 1:3 scaled structure is developed using IDARC2D modified in this study to evaluate several alternatives of weakening using rocking columns.

Seismic Evaluation and Retrofit of Concrete Buildings: A Practical Overview of the ATC 40 Document

The Applied Technology Council (ATC), with funding from the California Seismic Safety Commission developed the document, Seismic Evaluation and Retrofit of Concrete Buildings, commonly referred to as ATC 40. This two-volume, 612-page report provides a recommended procedure for the seismic evaluation and retrofit of concrete buildings. Although the focus is specifically on concrete buildings, the document provides information on emerging techniques applicable to most building types. This paper provides an introduction and overview of the document. The conceptual basis of the procedures is performance-based design using nonlinear static structural analysis. The ATC 40 document comprises a practical guide to the entire evaluation and retrofit process. Topics include performance objectives, seismic hazard, determination of deficiencies, retrofit strategies, quality assurance procedures, nonlinear static analysis using the capacity spectrum method, modeling recommendations, foundation effects, and response limits.

Large deflection analysis of structures by an improved combined finite element-transfer matrix method

An improved combined finite element-transfer matrix (IFE-TM) method is applied to the static analysis of structures with large displacement. In the present method, the transference of the state vectors from the left to the right in the combined finite element-transfer matrix method is changed into the transference of incremental stiffness equations of every section from the left to the right, in order to overcome the fault that the FE-TM method is generally applied to structures with a regular boundary. Furthermore, in the present method, the propagation of round-off errors occurring in recursive multiplications of the transfer and point matrices is avoided. A load incremental method is combined with modified Newton-Raphson method for the non-linear equations. A program ITNONDL-J based on this method is developed on the microcomputer IBM-PC/AT. Finally, numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for geometrically non-linear static analysis of structures with a random boundary.

Recent advances in reduction methods for nonlinear problems

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (a) selection of basis vectors in nonlinear static and dynamic problems (b) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (c) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.