Linear Elastic Structural Analysis Research Articles

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.

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.

Comparative dimensioning of plane timber truss by ABNT NBR 7190:1997 method and ABNT NBR 7190-1:2022 method

Wood, a renewable source and a material with excellent mechanical properties, is one of the oldest materials used in civil construction. In Brazil, its use is widespread in roof structures in the form of plane trusses. Given the Brazilian context of the growing presence of wood in structural systems, in addition to the normative updating processes, this study presents a comparison between calculation methods and possible increases in material consumption of wood for roof structure. The design methods compared are according to the recently published standard ABNT NBR 7190-1 (2022) and its previous version ABNT NBR 7190 (1997). The results were obtained via iTruss software, which includes linear-elastic structural analysis by the finite element method (FEM). It was concluded that the ABNT NBR 7190-1 (2022) presents a conservative dimensioning in relation to the previous version of 1997, favoring safety. However, there were no significant increases in wood consumption, demonstrating the efficiency of the revised version.

Design recommendations for the stability of transmission steel lattice towers

Lattice towers are extensively built in Europe and worldwide to serve telecommunication or power transmission purposes. Their members are usually made of equal leg angle profiles that are bolted at their extremities. Such types of towers are mainly designed to EN 1993-3-1 and EN 50341-1, based on a first-order linear elastic structural analysis of a truss structure. In this paper, an assessment of the current design approach is performed, where the tower has been simulated with a full non-linear finite element software, considering relevant imperfections as well as geometrical and material non-linearities. The importance of the second order effects in the analysis is underlined while the existence of an instability mode not properly covered directly by the norms, and usually therefore not checked, is highlighted. Two analytical models for the prediction of the critical load of this buckling mode are proposed and validated numerically. Both proposed models are rather easy to apply and may fill the gap in the existing design recommendations for lattice towers.

Numerical investigation into I-shape brace connections of conventional concentrically braced frames

In many low and moderate seismic regions, a low-ductility concentrically braced frame (CBF) is used as the seismic force resisting system for steel structures. The design of such CBFs is straightforward: all members and connections are designed based on the seismic force demand obtained through linear elastic structural analysis; capacity-based design and additional seismic detailing are not required. There is no designated energy-dissipating fuse in the lateral load-carrying path. Such CBFs are referred to as Conventional CBFs (CCBFs) in this study. In CCBFs, the brace-to-gusset connections are inherently weaker in tension than the adjoining gusset plates and braces. This occurs because both the gusset plates and the braces are selected on the basis of their respective compressive buckling resistances, and hence, typically have a much greater resistance in tension. Described herein is a numerical study of the popular flange plate bolted I-shape brace connection configuration. A high-fidelity finite element (FE) simulation procedure was developed and validated against laboratory test results. The resulting numerical models were created with the objective of improving our understanding of the inelastic response of these brace connections. The force transfer mechanism within the two branches of the connection was characterized. Significant nonuniform shear distribution was found to exist within the bolt group in the flange branch, which may be detrimental to the safe functioning of these bolts in the seismic design context. The loading eccentricity on the weld group was quantified. Recommendations on how to avoid brittle bolt shear rupture and premature weld fracture are proposed.

An interval finite element method for the analysis of structures with spatially varying uncertainties

Finite element analysis of linear-elastic structures with spatially varying uncertain properties is addressed within the framework of the interval model of uncertainty. Resorting to a recently proposed interval field model, the uncertain properties are expressed as the superposition of deterministic basis functions weighted by particular unitary intervals. An Interval Finite Element Method (IFEM) incorporating the interval field representation of uncertainties is formulated by applying an interval extension in conjunction with the standard energy approach. Uncertainty propagation analysis is performed by adopting a response surface approach which provides approximate explicit expressions of response bounds requiring only a few deterministic analyses. Then, the whole procedure is implemented in ABAQUS’ environment by coding User Subroutines and Python scripts.2D plane stress and bending problems involving uncertain Young's modulus of the material are analyzed. The accuracy of the proposed IFEM as well as response variability under spatially dependent uncertainty are investigated.

Dynamics of structures with uncertain-but-bounded parameters via pseudo-static sensitivity analysis

Abstract This paper deals with the analysis of linear-elastic structures with uncertain-but-bounded parameters subjected to deterministic dynamic loads. A novel procedure based on the use of sensitivity analysis in conjunction with classical modal superposition method is proposed. Specifically, a pseudo-static sensitivity analysis is performed to seek the combinations of the endpoints of the uncertain parameters which give the lower bound and upper bound of the response at each time instant. Among these, two combinations are selected as the most common ones over the time interval of interest in order to avoid the onerous updating of the uncertain parameters at each time instant. Then, the bounds of the response time-history are evaluated by performing two parallel deterministic modal analyses associated to the most common combinations of the extreme values of interval uncertainties. Numerical results demonstrate that the proposed method is more efficient than both the Interval Perturbation Method (IPM) and the classical combinatorial procedure. Furthermore, unlike the IPM, it allows the analysis of large-size structures exhibiting relatively large fluctuations of the uncertain parameters.

A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA

The paper presents an efficient and reliable implementation of numerical methods for constrained generalized eigenvalue problems, specialized for the modal analysis of linear elastic structures in a finite-element setting. The implementation, which takes into account the sparsity of the stiffness and mass matrices and the features of master-slave constraints, is based on open-source packages embedded in the finite-element code NOSA-ITACA. Numerical tests on historical building are performed, with the aims of calculating their vibration frequencies and mode shape vectors, comparing them to the results of a general purpose commercial code and assessing the accuracy of the tool developed.

Evaluation of Representative Loading Frequency for Linear Elastic Analysis of Asphalt Pavements

The mechanistic design of flexible pavement is usually done with linear elastic theory (LET); this process must use appropriate values of the equivalent asphalt concrete elastic modulus to evaluate stresses and strains in a linear elastic multilayer. The aim is to identify some relationships to estimate the value of loading frequency, representative of the real strain pulse frequency spectrum, to be used in calculating the stiffness modulus of the asphalt concrete layers. In this way, an equivalent linear elastic structural analysis can be conducted. To achieve this aim, many transient load simulations were performed with ViscoRoute software based on the viscoelastic model. After variables that affected the representative frequency value were detected, more than 215 variable combinations (representative of real conditions) were randomly generated. For each combination, viscoelastic analysis was conducted, and then the stiffness modulus and the corresponding loading frequency were backcalculated by minimizing the residuals between linear elastic and viscoelastic peak strains. The representative frequency values calculated for these configurations were related to the significant variables by means of a multivariate regression. The model was developed separately for each of the three directions according to the anisotropic behavior of pavement under moving loads. Finally, the procedure was validated by applying it to several climatic and load configurations of an existing pavement. A simple and useful tool is provided to take into account all significant parameters; the tool can be used in conjunction with LET for pavement design.

Mechanical and geometric advantages in compliant mechanism optimization

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism’s structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.

Performance Evaluation of Element-by-Element Operations for Linear Elastic Structural Analysis on Multi-core Architecture

Performance Evaluation of Element-by-Element Operations for Linear Elastic Structural Analysis on Multi-core Architecture

A rectangular finite element formulation

A finite element formulation for the static and dynamic analysis of linear-elastic space structures composed of plate- and beam-type members is presented in this study. In general, finite elements can be used efficiently for the analysis of linear-elastic structures with shear walls built by the use of tunnel forms. The element considered in the present study has six degrees of freedom at each node and an in-plane rotational degree of freedom, which makes it compatible with three-dimensional (3D) beam-type finite element models. The rigidity coefficients of the element are determined analytically. The element can be used with facility for the modeling of a shear wall with the connections of slab components. The finite element considered here yields highly accurate results with a very small number of elements. Convergence studies have been conducted on actual structures by using several models to check the performance of the rectangular finite elements. Acceptable results are obtained with coarse meshes and reasonable convergence is observed on the models tested. A special purpose computer program “TUNAL” developed for 3D analysis of linear-elastic structures and the finite element formulation is embedded within the program library. The validity of the assumptions and simplifications commonly made in the analysis of shear-wall-frame structures are investigated.

Asymptotic modelling theorems for the static analysis of linear elastic structures

The work presented here justifies the use of restraints with large positive and negative stiffness values to asymptotically model geometric constraints of a structure in linear structural analysis. Replacing constraints by very stiff restraints improves the versatility of variational methods such as the Rayleigh–Ritz method as the limitation on the choice of functions is removed. Based on recently published theorems on the existence of natural frequencies of systems with artificial restraints of positive and negative stiffness and their convergence towards the frequencies of the corresponding constrained systems, a proof is given to show that the displacement of a constrained structure caused by any action along its direction is approached and bracketed by the displacement of systems with artificial restraints of positive and negative stiffness (positive and negative penalty functions) as the magnitude of stiffness is increased. A procedure for the practical use of positive and negative penalty functions in static analysis of linear structures is also proposed.

A Meshless Method for Computational Stochastic Mechanics

This paper presents a stochastic meshless method for probabilistic analysis of linear-elastic structures with spatially varying random material properties. Using Karhunen-Loève (K-L) expansion, the homogeneous random field representing material properties was discretized by a set of orthonormal eigenfunctions and uncorrelated random variables. Two numerical methods were developed for solving the integral eigenvalue problem associated with K-L expansion. In the first method, the eigenfunctions were approximated as linear sums of wavelets and the integral eigenvalue problem was converted to a finite-dimensional matrix eigenvalue problem that can be easily solved. In the second method, a Galerkin-based approach in conjunction with meshless discretization was developed in which the integral eigenvalue problem was also converted to a matrix eigenvalue problem. The second method is more general than the first, and can solve problems involving a multi-dimensional random field with arbitrary covariance functions. In conjunction with meshless discretization, the classical Neumann expansion method was applied to predict second-moment characteristics of the structural response. Several numerical examples are presented to examine the accuracy and convergence of the stochastic meshless method. A good agreement is obtained between the results of the proposed method and the Monte Carlo simulation. Since mesh generation of complex structures can be far more time-consuming and costly than the solution of a discrete set of equations, the meshless method provides an attractive alternative to the finite element method for solving stochastic-mechanics problems.

Some controversial aspects of the seismic design of reinforced concrete building structures

Significant differences exist between the recommendations for seismic design of the codes and guidelines for reinforced concrete of different countries. Performance criteria for building structure to avoid unacceptable damage during various levels of earthquake hazard need to be refined. More accurate recommendation for the effective flexural rigidity of reinforced concrete members are required for linear elastic structural analysis to enable better estimates of the periods of vibration and the lateral deflections of statically indeterminate structures including the effects of cracking of concrete. Current code recommended values for flexural rigidity will generally lead to estimates of the periods of vibration and lateral deflections, which are on the low side. The capacity design approach to ensure the most appropriate mechanism of yielding will occur in the event of a severe earthquake is generally recognized by codes but to varying degrees of clarity, and the degrees to which capacity design is incorporated in each code varies significantly. High strength concrete and high strength non-prestressed steel reinforcement can be used in the design of buildings but the brittle behaviour of high strength concrete and the unusable yield strength of high strength steel reinforcement need to be considered. Important differences between codes exist in the rules for the quantity of confining reinforcement placed in reinforced concrete columns to ensure ductile behaviour. Significant differences also exist between the quantities of shear and confining reinforcement required in beam-column joints and in the anchorage of length of longitudinal reinforcement passing through beam-column joints. Precast concrete structures can be designed successfully for earthquake resistance but design codes in seismic regions contain provisions for precast concrete to varying degrees.

An element-free Galerkin method for probabilistic mechanics and reliability

A stochastic element-free Galerkin method was developed for reliability analysis of linear-elastic structures with spatially varying random material properties. A random field representing material properties was discretized into a set of random variables with statistical properties obtained from the statistical properties of random field. In conjunction with meshless formulations, the first-order reliability method was employed to predict the full probabilistic characteristics of a structural response. Unlike the stochastic finite element method, the stochastic mesh-free method does not require a structured mesh, instead only a scattered set of nodal points is required in the domain of interest. As well, there is no need for fixed connectivities between nodes. Numerical examples show good agreement between the results of the developed method and Monte Carlo simulation. Furthermore, the stochastic meshless method provides convergent solutions of the probability of failure. Since mesh generation of complex structures can be far more time-consuming and costly effort than solution of a discrete set of equations, the developed meshless method provides an attractive alternative to finite element method for solving stochastic-mechanics problems.

Application of linear structural analysis program for steel frame ultimate limit state analysis

This paper describes the feasibility of applying a modified linear structure analysis computer program in the ultimate limit state design of unbraced steel frames. The elastic–plastic hinge zone concept and the linear elastic structural analysis computer program SAP90, are used to simplify the nonlinear steel frame structural analysis model. Most steel structures are designed by plastic theory, called ‘ultimate limit state design’. In practice, most steel structure analysis is performed by linear elastic computer programs that do not take into account either inelastic behavior or calculation of the ultimate strength. Herein, a modified analysis approach is presented and its design implications discussed. The results obtained from the modified approach are provided and compared with both experimental data and the inelastic structural analysis computer program DRAIN-2DX with respect to the ultimate strengths and the lateral displacements of unbraced steel frames. Copyright © 1999 John Wiley & Sons, Ltd.

A constraint-based approach for qualitative matrix structural analysis

AbstractQualitative physics, a subfield of artificial intelligence, adapts intuitive and non-numerical reasoning for descriptive analysis of physical systems. The application of a set-based qualitative algebra to matrix analysis (QMA) allows for the development of a qualitative matrix stiffness methodology for linear elastic structural analysis. The unavoidable introduction of arithmetic ambiguity requires the reinforcement of physical constraints complementary to standard matrix operations. The overall analysis technique incorporates such constraints within the set-based framework with logic programming. Truss, beam, and frame structures demonstrate constraint relationships, which prune spurious solutions resulting from qualitative arithmetic relations. Though QMA is not a panacea for all structural applications, it provides greater insight into new notions of physical analysis.

Three-dimensional thermal structural analysis of a swept cowl leading edge subjected to skewed shock-shock interference heating

A three-dimensional flux-based thermal analysis method has been developed and its capability is demonstrated by predicting the transient nonlinear temperature response of a swept cowl leading edge subjected to intense three-dimensional aerodynamic heating. The predicted temperature response from the transient thermal analysis is used in a linear elastic structural analysis to determine thermal stresses. Predicted thermal stresses are compared with those obtained from a two-dimensional analysis which represents conditions along the chord where maximum heating occurs. Results indicate a need for a three-dimensional analysis to predict accurately the leading edge thermal stress response.

Nonstationary pandom vibpation analysis of linear elastic structures with finite element method

At present, the finite element method is an efficient method for analyzing structural dynamic problems. When the physical quantities such as displacements and stresses are resolved in the spectra and the dynamic matrices are obtained in spectral resolving form, the relative equations cannot be solved by the vibration mode resolving method as usual. For solving such problems, a general method is put forward in this paper. The excitations considered with respect to nonstationary processes are as follows: $$P(t) = \left\{ {P_1 (t)} \right\},{\text{ }}P_1 (t) = a_1 (t)P_1^0 (t),$$ a1(t) is a time function already known. We make Fourier transformation for the discretized equations obtained by finite element method, and by utilizing the behaviour of orthogonal increment of spectral quantities in random process[1], some formula of relations about the spectra of excitation and response are derived. The cross power spectral denisty matrices of responses can be found by these formulas, then the structrual safety analysis can be made. When a(1)=1 (i=1.2, ...,n), the method stated in this paper will be reduced to that which is used in the special case of stationary process.