Interaction of geometric and material nonlinearities in stainless steel frames

Pseudo-static test on stainless steel frame with high-strength bolted extended endplate joint

Beam-like, architected microstructures (BAMs) can be used in various functional applications, such as micro-electro-mechanical systems (MEMS), energy harvesting, actuation, etc. Designing with high aspect ratios under large deformations, BAMs typically experience severe buckling instability. Therefore, it is of necessity to investigate the mechanical behaviors with respect to the geometric and material nonlinearities. This paper proposes a bilinear size-dependent model using the modified couple stress theory to full formulate the buckling response of the BAMs. Buckling-induced large deformation is studied using the geometric nonlinearity, and the recoverability is investigated based on the material nonlinearity. Experiments and numerical simulations are conducted to validate the theoretical results at the macroscale and microscale, respectively, and satisfactory agreements are obtained. Parametric studies are carried out to study the effects of the material length scale factor-to-thickness ratio χ=lt (i.e., geometric nonlinearity) and plastic factor η (i.e., material nonlinearity). χ and η are further discussed with respect to the effective bending stiffness B¯PAM and volume V¯PAM of the microstructures. The theoretical model presented in this study can be used to predict and tune the mechanical response of BAMs with different architected webbing patterns.

Dynamic soil–structure interaction (SSI) represents an interdisciplinary subject characterized by complex geometrical and material nonlinearities affecting both the soil and the structural components of the system under study. In the current practice, SSI problems are often solved using the so-called substructure method based on decomposing the superstructure-foundation-soil system into two subsystems whose response is determined independently. The direct method is a more general procedure to tackle SSI problems which is in principle capable of accounting for both soil and structural nonlinearities. Despite this generality, most of the current computational platforms are specialized either for structural applications or for geotechnical applications. Whereas the formers are capable to accurately reproduce the nonlinear response of the structural elements, they are usually poor in modeling soil nonlinear behaviour especially under earthquake loading. On the other hand, the latter do the reverse: they are advanced in modeling soil response but typically rough in reproducing the behaviour of the structural components of the system. Inevitably, all structures interact with the ground and therefore the need to model material and geometric nonlinearities maybe important both in the ground and structural elements. The variation of the stiffness mismatch between soil and structural elements during ground motions is one of the most influential parameters for the assessment of the kinematic component in SSI problems. The variation of the stiffness ratio is mainly governed by material nonlinearity that can develop in either the soil or the structural parts of the system. This paper presents a nonlinear constitutive model for beam elements that is compatible with performance–based earthquake engineering principles because it is capable to simulate the cyclic degradation of mechanical properties and to assess the damage suffered by the structural system. The proposed model is based on distributed plasticity and can be easily implemented in any computational platform allowing the use of an explicit solver. The article describes the theoretical aspects of the model. Validation and application of the model to the solution of a dynamic soil–structure interaction problem where the nonlinear behaviour of geomaterials is coupled with the inelasticity of structural elements, are presented in a companion paper (Andreotti and Lai in Bull Earthq Eng 2017).

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

Nonlinear analysis of 3-D steel frames

Nonlinear aerostatic stability analysis of suspension bridges

Ehab Ellobody? Department of Structural Engineering, Faculty of Engineering, Tanta University, Tanta, Egypt Ben Young? Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong (Received September 13, 2006, August 13, 2007) Abstract. The investigation on the behaviour of cold-formed stainless steel non-slender circular hollow section columns is presented in this paper. The normal strength austenitic stainless steel type 304 and the high strength duplex materials (austenitic-ferritic approximately equivalent to EN 1.4462 and UNS S31803) were considered in this study. The finite element method has been used to carry out the investigation. The columns were compressed between fixed ends at different column lengths. The geometric and material nonlinearities have been included in the finite element analysis. The column strengths and failure modes were predicted. An extensive parametric study was carried out to study the effects of normal and high strength materials on cold-formed stainless steel non-slender circular hollow section columns. The column strengths predicted from the finite element analysis were compared with the design strengths calculated using the American Specification, Australian/New Zealand Standard and European Code for cold-formed stainless steel structures. The numerical results showed that the design rules specified in the American, Australian/New Zealand and European specifications are generally unconservative for the cold-formed stainless steel non-slender circular hollow section columns of normal and high strength materials, except for the short columns and some of the high strength stainless steel columns. Therefore, different values of the imperfection factor and limiting slenderness in the European Code design rules were proposed for cold-formed stainless steel non-slender circular hollow section columns.

Element interaction of cold-formed stainless steel cross-sections subjected to major axis bending

Second-order inelastic analysis of cable-stayed bridges

An analysis is described that models the behavior of planar prestressed concrete cable‐stayed bridges up to failure taking into account geometric and material nonlinearities. The geometric nonlinearities arise from cable sag, large deformations of the system, and from the shift of the centroid of the deck section caused by the material or by cracking of the concrete. The effect of the axial forces on the stiffness of the members is also considered. Material nonlinearities are encountered when one or more of the structure components, namely the stay cables, prestressing tendons, the reinforcement, or the concrete, exceed their elastic limits. Parametric studies are made on cable‐stayed bridges with the following cable arrangements: fan, semifan and harp‐type cable arrangement. To demonstrate the influence of the different types of nonlinearity on the internal forces and reactions three analyses were performed—namely elastic, geometric nonlinear, and geometric and material nonlinear analyses—and the results...

Geometrical nonlinearity arises from the continuous change of shape under increasing loads on thin or long span members, and the materials nonlinearity due to the nonlinear behavior of the materials composing the structural element. In this study the finite element method is used to analyze fibrous reinforced concrete slabs, material and geometric nonlinearities were considered. Concrete is represented by degenerate quadratic thick shell element. Concrete behavior in compression is modeled by elastic perfectly plastic or strain hardening plasticity. A tensile strength criterion is used to follow crack initiation and propagation. A parabolic stress degradation function, which is based on the fracture energy concept, is used to model the tension stiffening effect of steel fibers. The reinforcement is considered as smeared within the concrete layers, and assumed as either an elastic perfectly plastic material or as an elastic-plastic material with linear strain hardening. Von Karman assumptions which is based on the total Lagrangian approach is used for the geometric nonlinearity. The numerical results using for both normal and lightweight fiber reinforced concrete slabs were predicted satisfactorily. The average predicted failure load of the investigated cases to the experimental failure load was 0.899 with a standard deviation of 0.092.

Sensitivity analysis and shape optimization in nonlinear solid mechanics

Selection of a suitable material is of prime importance in designing and fabrication of the hybrid agricultural sprayer. Material plays an important role as it affects factors such as function, mechanical properties, quality, manufacturability, endurance, performance and cost of the hybrid agricultural sprayer. In this research paper, the solid modelling of hybrid agricultural sprayer has been done on SolidWorks and suitable material is selected by comparing static structural analysis of aluminium, mild steel, stainless steel, epoxy carbon and epoxy E-glass UD-based frames on ANSYS workbench and properties such as density and yield strength. The deformation, equivalent stress and equivalent strain, obtained through analysis on ANSYS workbench, and other properties such as density and yield strength cost are compared for aluminium, mild steel, stainless steel, epoxy carbon and epoxy E-glass UD-based frames to determine the suitable material for the frame of the hybrid agricultural sprayer. Thus, by comparing aluminium, mild steel, stainless steel, epoxy carbon and epoxy E-glass UD-based frames, this research paper determines the appropriate material for the frame of the hybrid agricultural sprayer.

Experimental study on stainless steel tubular members under cyclic loading

A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics