Search results

Design engineers use the term load path to describe, in general terms, the way in which loads path through a structure from the points of application to the points where they are reacted. In contrast, stress trajectories are more clearly identified by the direction of the principal stress vectors at a point. The first author proposed a simple definition of the term load path in 1995 and proposed procedures to determine load paths from two‐dimensional finite element solutions. In this paper, the concept of load paths will be further explored and related to stress trajectories and Michell structures. The insight given when determining the load transfer near a pin‐loaded hole will be demonstrated. In addition a cantilevered beam will be considered and an introduction to plotting load paths in three‐dimensional structures is given.

The determination of load paths is an essential element of structural design. Load paths provide insight into the way the structure is performing its prescribed function. They can also indicate possibilities for shape optimization and the effect of component modification or damage. They are relatively easy to define in simple structures such as trusses which comprise a finite number of clearly defined members which carry only axial load. The load path is given simply by tracing the higher axial loads through the structure. However, for continua such as plates or solids, there is currently no systematic procedure for determining the path of load from the point of application to the constrained boundaries. This paper addresses the problem of defining the path of loads in plates with geometric discontinuities and in simple joints. The theory associated with the determination of the load path is first introduced, and then integrated into a finite element package to provide pictorial contours.

The purpose of this paper is to describe a post‐processing procedure for defining load paths and a load bearing topology using the stresses from a finite element analysis.

Cauchy stress vectors and a Runge‐Kutta algorithm are used to identify the paths being followed by load components aligned with the coordinate axes. An algorithm is then defined which identifies an efficient topology that will carry the loads by straightening the paths.

The aim of the algorithm is to provide insight into the way a structure is carrying loads by identifying the material most effective in performing the load transfer. The procedure is applied to a number of structures to demonstrate its applicability to structural design.

The examples demonstrate an insight of structural behavior that is useful at the conceptual stage of the design process. The load paths identify load transfer and warn the designer of the creation of bending moments and the location of features such as holes on the load path. They also demonstrate that the new procedures can provide suggestions for alternate topologies for the load bearing structure.

The load path theory has been published elsewhere. The new work in this paper is the definition of the Runge‐Kutta algorithm to define the paths and the algorithm to identify the topology performing the load transfer.

A procedure for plotting load paths and load flow in structures from a finite element analysis is described. The load flow is indicated by pointing vectors and the load paths are determined by plotting contours tangent to these vectors. The procedure is applied to assembled structures. An explanation is given for “eddies” that can appear in regions not contributing to the load path.

A large number of data have proved that under the same von Mises equivalent strain condition, the fatigue life under multiaxial non-proportional loading is often much lower than the life under multiaxial proportional loading. This is mainly due to the influence of the non-proportional loading path and the additional hardening effect, which lead to a sharp decrease in life.

The modulus attenuation effect is used to modify the static hardening coefficient, and the predicted value obtained is closer to the additional hardening coefficient obtained from the experiment. A fatigue life model can consider non-proportional paths, and additional hardening effects are proposed. And the model uses multiaxial fatigue test data to verify the validity and adaptability of the new model. The life prediction accuracy and material application range are satisfactory.

Because loading path and additional hardening of the material affect fatigue life, a new multiaxis fatigue life model based on the critical plane approach is proposed. And introducing a non-proportional additional damage coefficient, the joint influence of the load path and the additional hardening can be considered. The model's life prediction accuracy and material applicability were verified with multiaxial fatigue test data of eight materials and nine loads compared with the prediction accuracy of the Kandil–Brown–Miller (KBM) model and Fatemi–Socie (FS) model.

The physical meaning of the new model is clear, convenient for practical engineering applications.

This paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths.

First, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program.

The method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure.

Original features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

The purpose of this paper is to present a constraint and corresponding algorithm enhancing the evolutionary structural optimization (ESO) method, aiming to circumvent its structure break down problem in some special cases, such as the tie-beam problem.

A virtual soft material introduced to an element will change the stiffness of the element and may consequently change the stress distribution of that element and its neighbors. With this property, the virtual stiffness of the selected element is calculated and the threshold of the stress changes is derived. The stress threshold is used to evaluate the role of an element on the load path and therefore decide the contribution of the element to the structure. Adding this checking operation into the original ESO iterations enables validation of element removal.

The reason for structure break down with the ESO method is that the element removal criterion of ESO only works for certain optimal objectives. It cannot guarantee that the structure does not fail. The proposed operation offers a stronger and stricter constraint condition for ESO’s element removal process, preventing the structure from breaking down in some special cases.

The tests on several examples reported in the literature show that the proposed method has the same ability to achieve an optimum solution as the original ESO methods do, while avoiding incorrect deletion of structurally important elements. The benchmark tie-beam problem is solved successfully with this algorithm. The method can be used in other situations as well.

The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non‐linear material behaviour using a simple damage model. The extended CDM is useful to detect instability points using a prediction of the critical displacement field and a secant load‐displacement relationship accounting for material non‐linearities. Examples of application of CDM to the instability analysis of structures using bar and solid finite elements are presented.

The generality of the genetic search in the light of proper coding schemes, together with its non‐gradient‐based search, has made it popular for many discrete problems including structural optimization. However, the required computational effort increases as the cardinality of the search space and the number of design variables increase. Memetic algorithms are formal attempts to reduce such a drawback for real‐world problems incorporating some kind of problem‐specific information. This paper aims to address this issue.

In this paper both Lamarckian and Baldwinian approaches for meme evolution are implemented using the power of graph theory in topology assessment. For this purpose, the concept of load path connectivity in frame bracing layouts is introduced and utilized by the proposed graph theoretical algorithms. As an additional search refinement tool, a dynamic mutation band control is recommended. In each case, the results are studied via a set of ultimate design family rather than one pseudo optimum. The method is further tested using a number of steel frame examples and its efficiency is compared with conventional genetic search.

Here, the problem of bracing layout optimization in steel frames is studied utilizing a number of topological guidelines.

The method of this paper attempts to reduce the computational effort for optimal design of real‐world problems incorporating some kind of problem‐specific information.