Multiple Loading Conditions Research Articles

A High Performance Multifrontal Code for Linear Solution of Structures Using Multi-Core Microprocessors

A multifrontal code is introduced for the efficient solution of the linear system of equations arising from the analysis of structures. The factorization phase is reduced into a series of interleaved element assembly and dense matrix operations for which the BLAS3 kernels are used. A similar approach is generalized for the forward and back substitution phases for the efficient solution of structures having multiple load conditions. The program performs all assembly and solution steps in parallel. Examples are presented which demonstrate the code's performance on single and dual core processor computers.

Discrete structural optimization by removing redundant material

A very simple method for finding the minimum weight of a structure designed from a list of available parameters is presented. The structure can be subjected to multiple loading conditions with constraints imposed on displacements, stresses and eigenfrequency. The method consists of a recursive removal of redundant material, starting from the heaviest structure. The number of analyses required is a factor of 102 less than for most stochastic methods. The knowledge needed for application of the method is limited to the finite-element method.

Development of an in vitro three dimensional loading-measurement system for long bone fixation under multiple loading conditions: a technical description

The purpose of this investigation was to design and verify the capabilities of an in vitro loading-measurement system that mimics in vivo unconstrained three dimensional (3D) relative motion between long bone ends, applies uniform load components over the entire length of a test specimen, and measures 3D relative motion between test segment ends to directly determine test segment construct stiffness free of errors due to potting-fixture-test machine finite stiffness.Intact equine cadaveric radius bones, which were subsequently osteotomized/ostectomized and instrumented with bone plates were subjected to non-destructive axial, torsion, and 4-point bending loads through fixtures designed to allow unconstrained components of non-load associated 3D relative motion between radius ends. 3D relative motion between ends of a 50 mm long test segment was measured by an infrared optical tracking system to directly determine its stiffness. Each specimen was then loaded to ultimate failure in either torsion or bending. Cortical bone cross-section diameters and published bone biomechanical properties were substituted into classical mechanics equations to predict the intact test segment theoretical stiffness for comparison and thus loading-measurement system verification.Intact measured stiffness values were the same order of magnitude as theoretically predicted. The primary component of relative motion between ends of the test segment corresponded to that of the applied load with the other 3D components being evident and consistent in relative magnitude and direction for unconstrained loading of an unsymmetrical double plate oblique fracture configuration. Bone failure configurations were reproducible and consistent with theoretically predicted.The 3D loading-measurement system designed: a) mimics unconstrained relative 3D motion between radius ends that occurs in clinical situations, b) applies uniform compression, torsion, and 4-point bending loads over the entire length of the test specimen, c) measures interfragmentary 3D relative motion between test segment ends to directly determine stiffness thus being void of potting-fixture-test machine stiffness error, and d) has the resolution to detect differences in the 3D motion and stiffness of intact as well osteotomized-instrumented and ostectomized-instrumented equine radii.

A topology optimization based model of bone adaptation

A novel topology optimization model based on homogenization methods was developed for predicting bone density distribution and anisotropy, assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness. The feasibility and efficiency of this method were tested on a 2D model for a proximal femur under single and multiple loading conditions. The main aim was to compute homogenized optimal designs using an optimal laminated microstructure. The computational results showed that high bone density levels are distributed along the diaphysis and form arching struts within the femoral head. The pattern of bone density distribution and the anisotropic bone behavior predicted by the model in the multiple load case were both in good agreement with the structural architecture and bone density distribution occurring in natural femora. This approach provides a novel means of understanding the remodeling processes involved in fracture repair and the treatment of bone diseases.

Constitutive modelling of viscoplasticity in a nickel-based superalloy at high temperature

Inelastic deformation behaviour of an advanced nickel-base superalloy has been investigated at 650 °C under multiple step cyclic and dwell loading conditions and for different strain rates. A viscoplastic constitutive model with strain range dependent cyclic hardening has been proposed. The model is based on the unified Chaboche model modified to account for non-linear kinematic hardening and plastic strain memory. For uniaxial loading, the initial estimates of material parameters were derived from simple strain controlled tests whilst a optimization procedure has been used to obtain the final material parameters. In this paper description of the proposed model, interpretation of the parameters and the optimisation procedure are presented. The predictions of the model are compared with the results for dwell loading tests with different strain rates, cyclic loading tests with selected strain ranges and creep tests under three stress levels. The results predictions show notable improvement compared to the predictions from previous work with respect to stress amplitude. The correlation coefficients and sensitivities of the optimised material parameters were also examined, in justification for the new model.

Multilevel optimization in aircraft structural design evaluation

Changes of the structural design are one of the essentials in the investigation and optimization of alternative and innovative aircraft concepts. In this paper the choice of an appropriate design is seen as an optimization problem and solved by the application of a multilevel optimization procedure based on detailed Finite Element models of certain structural parts. The design is variable by its principle layout, its material and its dimensions. At the top level an Evolution Strategy drives the topology parameters. The second level of the optimization procedure is based on the deterministic, gradient-based optimization method of MSC.Nastran ® Sol200 that is used to optimize thicknesses and cross-sections of the model with respect to different design constraints. The model generation is based on Patran PCL-routines. A parallel evaluation is used to increase calculation speed. Two examples are presented in this context. The first one shows advantages of the multilevel approach in simultaneous sizing and topology optimization of a generic framework structure. The second example is an application to a structural design optimization of a Blended Wing Body aircraft fuselage structure. This example shows the full scope of the method by consideration of metal and composite designs in single, double and sandwich layout under multiple load and constraint conditions.

On the maximization of the fundamental eigenvalue in topology optimization

The paper considers a classic formulation of the topology optimization problem of discrete or discretized structures. The objective function to be maximized is the smallest natural frequency of the structure. We develop non-heuristic mathematical models paying special attention to the situation when some design variables take zero values. These models take into account multiple load conditions, equilibrium of forces, constraints on compliance and volume, and the effect of possible non-structural mass. We discuss serious obstacles for a successful numerical treatment of this formulation such as non-Lipschitzean behavior and even discontinuity of the objective function. As a cure, we present an equivalent reformulation as a bilinear semidefinite programming problem without the pitfalls of the original problem. An algorithm is presented for finding an approximation of a globally optimal solution up to a user-defined accuracy. The key ingredient of this algorithm is the treatment of a sequence of linear semidefinite programs. Numerical examples are provided for truss structures. Examples of both academic and larger size illustrate the theoretical results achieved and demonstrate the practical use of this approach. We conclude with an extension on multiple non-structural mass conditions.

Load Path U* Analysis of Structures under Multiple Loading Conditions

The concept of the parameter U* has been introduced by the authors to express load transfer in structures. In this paper, an extended definition of U* is introduced for structures under multiple loadings. The new expression of U* with the matrix formulation of internal stiffness can effectively be applied to an efficient calculation of U* distribution. Examples of U* calculation for an actual truck cab structure under multiple loading are demonstrated. Calculation results of U* for cases under multiple loading condition and single loading condition are compared, and the applicability of St. Venant's principle concerning U* distribution is discussed.

Truss topology optimization with discrete design variables—Guaranteed global optimality and benchmark examples

This paper considers the problem of optimal truss topology design subject to multiple loading conditions. We minimize a weighted average of the compliances subject to a volume constraint. Based on the ground structure approach, the cross-sectional areas are chosen as the design variables. While this problem is well-studied for continuous bar areas, we consider in this study the case of discrete areas. This problem is of major practical relevance if the truss must be built from pre-produced bars with given areas. As a special case, we consider the design problem for a single available bar area, i.e., a 0/1 problem. In contrast to the heuristic methods considered in many other approaches, our goal is to compute guaranteed globally optimal structures. This is done by a branch-and-bound method for which convergence can be proven. In this branch-and-bound framework, lower bounds of the optimal objective function values are calculated by treating a sequence of continuous but non-convex relaxations of the original mixed-integer problem. The main effect of using this approach lies in the fact that these relaxed problems can be equivalently reformulated as convex problems and, thus, can be solved to global optimality. In addition, these convex problems can be further relaxed to quadratic programs for which very efficient numerical solution procedures exist. By exploiting this special problem structure, much larger problem instances can be solved to global optimality compared to similar mixed-integer problems. The main intention of this paper is to provide optimal solutions for single and multiple load benchmark examples, which can be used for testing and validating other methods or heuristics for the treatment of this discrete topology design problem.

Thermal, electrical, mechanical coupled mechanics for initial buckling analysis of smart plates and beams using discrete layer kinematics

Non-linear behavior of smart structures is of interest to researchers due to the possibilities for the elaboration of more effective actuators and sensors based on piezoelectric materials. The aim of the present work, is to present an integrated approach for the buckling behavior of smart beams and plates under multiple loading conditions. In order to present an accurate analysis, a coupled constitutive formulation between thermal, electrical and mechanical fields is elaborated incorporating non-linearity due to large displacements. An 8-node plate element was implemented in combination with discrete layer kinematics (LW) for the through-the-thickness representation of the structure. The issues of the critical buckling load under different electrical conditions as well as thermal and electrical loading are also presented. Experimental results contribute to the verification of the accuracy of the numerical analysis results and of the coupling mechanics in general.

Optimization of structures with nonlinear behavior using equivalent loads

Nonlinear Response Optimization using the Equivalent Loads (NROEL) method/algorithm is proposed to perform optimization of non-linear response structures. The conventional method spends most of the design time on nonlinear analysis. The NROEL algorithm makes the equivalent load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent loads are defined as the loads in linear analysis, which generate the same response fields as those in nonlinear analysis. The algorithm is validated for convergence and optimality. The proposed algorithm is applied to a simple mathematical problem to verify the convergence and the optimality. The NROEL algorithm is applied to several structural problems with geometric and/or material nonlinearity. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed NROEL method is found to be very efficient and good solutions are derived.

Aggregate production: Fines generation during rock crushing

The energy required to crush rocks is proportional to the amount of new surface area that is created; hence, a very important percentage of the energy consumed to produce construction aggregates is spent in producing non-commercial fines. Data gathered during visits to quarries, an extensive survey and laboratory experiments are used to explore the role of mineralogy and fracture mode in fines production during the crushing of single aggregates and aggregates within granular packs. Results show that particle-level loading conditions determine the failure mode, resulting particle shape and fines generation. Point loading (both single particles and grains in loose packings) produces clean fractures and a small percentage of fines. In choked operations, high inter-particle coordination controls particle-level loading conditions, causes micro-fractures on new aggregate faces and generates a large amount of fines. The generation of fines increases when shear is imposed during crushing. Aggregates produced in current crushing operations show the effects of multiple loading conditions and fracture modes. Results support the producers' empirical observations that the desired cubicity of aggregates is obtained at the expense of increased fines generation when standard equipment is used.

Evolutionary multi-objective optimization of the design and operation of water distribution network: total cost vs. reliability vs. water quality

An expanded rehabilitation of the hypothetical water distribution network of Anytown, USA is considered. As well as pipe rehabilitation decisions, tank sizing, tank siting and pump operation schedules are considered as design variables. Inclusion of pump operation schedules requires consideration of water system operation over the demand pattern period. Design of distribution storage facilities involves solving numerous issues and trade-offs such as locations, levels and volume. This paper investigates the application of multi-objective evolutionary algorithms in the identification of the pay-off characteristic between total cost, reliability and water quality of Anytown's water distribution system. A new approach is presented for formulation of the model. To provide flexibility, the network must be designed and operated under multiple loading conditions. The cost of the solution includes the capital costs of pipes and tanks as well as the present value of the energy consumed during a specified period. Optimization tends to reduce costs by reducing the diameter of, or completely eliminating, pipes, thus leaving the system with insufficient capacity to respond to pipe breaks or demands that exceed design values without violating required performance levels. Here a resilience index is considered as a second objective to increase the hydraulic reliability and the availability of water during pipe failures. Considering reliability as one of the objectives in the optimization process will decrease the level of vulnerability for the solutions and therefore will result in robust networks. However, oversized distribution mains and storage tanks will have adverse effects on water age with negative effects on water quality due to low flow velocity and little turnover, respectively. Therefore, another objective in the design and operation of distribution systems with storage facilities is the minimization of residence time, thus minimizing deterioration in water quality, which is directly associated with the age of water. Residence time must include not only the time in tanks but also the travel time before and after the water's entry into the storage facilities. The residence time of the water in the network is considered as a surrogate measure of water quality. Results are presented for the pay-off characteristics between total cost, reliability and water quality, for 24 h design and five loading conditions.

Metastatic Burst Fracture Risk Assessment Based on Complex Loading of the Thoracic Spine

The mechanical integrity of vertebral bone is compromised when metastatic cancer cells migrate to the spine, rendering it susceptible to burst fracture under physiologic loading. Risk of burst fracture has been shown to be dependent on the magnitude of the applied load, however limited work has been conducted to determine the effect of load type on the stability of the metastatic spine. The objective of this study was to use biphasic finite element modeling to evaluate the effect of multiple loading conditions on a metastatically-involved thoracic spinal motion segment. Fifteen loading scenarios were analyzed, including axial compression, flexion, extension, lateral bending, torsion, and combined loads. Additional analyses were conducted to assess the impact of the ribcage on the stability of the thoracic spine. Results demonstrate that axial loading is the predominant load type leading to increased risk of burst fracture initiation, while rotational loading led to only moderate increases in risk. Inclusion of the ribcage was found to reduce the potential for burst fracture by 27%. These findings are important in developing a more comprehensive understanding of burst fracture mechanics and in directing future modeling efforts. The results in this study may also be useful in advising less harmful activities for patients affected by lytic spinal metastases.

The usage of optical fibers for damage detection in ballistic protection composite laminates

This paper describes the procedure of embedding fiber optic sensors in laminar thermoplastic composite material, as well as damage investigation after ballistic loading. Thermoplastic-reinforced composite materials were made for increased material damage resistance during ballistic loading. Damage inside the composite material was detected by observing the intensity drop of the light signal transmitted through the optical fibers. Experimental testing was carried out in order to observe and analyze the response of the material under various load conditions. Different types of Kevlar reinforced composite materials (thermoplastic, thermo reactive and thermoplastic with ceramic plate as the impact face) were made. Material damage resistance during ballistic loading was investigated and compared. Specimens were tested under multiple load conditions. The opto-electronic part of the measurement system consists of two light-emitting diodes as light sources for the optical fibers, and two photo detectors for the light intensity measurement. The output signal was acquired from photo detectors by means of a data acquisition board and personal computer. The measurements showed an intensity drop of the transmitted light signal as a result of the applied loading on composite structure for all the optical fibers. All the diagrams show similar behavior of the light signal intensity. In fact, all of them may be divided into three zones: the zone of penetration of the first composite layer, the bullet traveling zone through the composite material till its final stop, and the material relaxation zone. The attenuation of the light signal intensity during impact is caused by the influence of the applied dynamic stress on the embedded optical fibers. The applied stress caused micro bending of the optical fiber, changes in the shape of the cross-section and the unequal changes of the indices of refraction of the core and cladding due to the stress-optic effect. The main goal of the experiment was to develop a system for thermoplastic composite structure health monitoring during real life exploitation. The results of the experiments confirmed that optical fibers could be applied as intensity sensors in the real-time monitoring of structural changes in thermoplastic laminar composite materials under ballistic loading. The light signal intensity drops in an optical fiber in response to the applied loading on the composite material.

複数の載貨状態における造波抵抗低減に関する研究

複数の載貨状態における造波抵抗低減に関する研究

A new hybrid fuzzy-goal programming scheme for multi-objective topological optimization of static and dynamic structures under multiple loading conditions

This work presents a hybrid fuzzy-goal multi-objective programming scheme for topological optimization of continuum structures, in which both static and dynamic loadings are considered. The proposed methodology fortopological optimization first employs a fuzzy-goal programming scheme at the top level for multi-objective problems with static and dynamic objectives. For the static objective with multi-stiffness cases in the fuzzy-goal formulation, a hybrid approach, involving a hierarchical sequence approach or a hierarchical sequence approach coupled with a compromise programming method, is especially suggested for the statically loaded multi-stiffness structure at the sublevel. Concerning dynamic optimization problems of freevibration cases, nonstructural mass, oscillation of the objective function, and repeated eigenvalues are also discussed. Solid Isotropic Material with Penalization density–stiffness interpolation scheme is used to indicate the dependence ofmaterial modulus upon regularized element densities. The globally convergent version of the method of moving asymptotes and the sequential linear programming method areboth employed as optimizers. Several applications have been applied to demonstrate the validation of the presented methodologies.

선형 등가정하중을 이용한 비선형 거동 구조물의 최적설계 (I) - 알고리듬 -

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. The conventional method spends most of the total design time on nonlinear analysis. The NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The proposed algorithm is applied to a simple mathematical problem to verify the convergence and the optimality.

An analysis of multiple two-step fatigue loading

Murakami and Matsuda have carried out multiple two-step tests using axially loaded cylindrical specimens of a 0.46% carbon steel. The specimens were pre-cracked and heat-treated to develop closure-free starter cracks ranging from 100 to 1000 μm in length. S/ N curves were developed under axial loading at R=−1 for each starter crack length. In the multiple two-step tests, one stress level was above the run-out stress level for that particular initial crack length, and the other level was below the run-out stress level. The loading pattern involved the application of one high-stress cycle followed by 40 low-stress cycles. This pattern was repeated until the cracks propagated to failure. Damage summations based upon an extrapolation of the upper portions of the S/ N curves to the lower stress level were of the order of 0.2. In the present paper, these data are analyzed using a modified LEFM approach. The modifications include a correction for elastic–plastic behavior, consideration of the endurance limit-threshold interrelation (Kitagawa effect), and consideration of the development of crack closure in the wake of an initially closure-free crack. The method is able to predict crack growth behavior under multiple two-step loading conditions fairly well. It is found that a principal role of the repeated application of the lower stress is not to propagate the crack, but to reduce the crack closure level and thereby facilitate an accelerated crack growth at the higher stress level.

Trade-off between Total Cost and Reliability for Anytown Water Distribution Network

This paper investigates the application of multiobjective evolutionary algorithms to the identification of the payoff characteristic between total cost and reliability of a water distribution system using the well-known Anytown network as an example. An expanded rehabilitation problem is considered where the design variables are the pipe rehabilitation decisions, tank sizing, tank siting, and pump operation schedules. To provide flexibility, the network is designed and operated under multiple loading conditions. Inclusion of pump operation schedules requires consideration of water system operation over an extended period. The cost of the solution includes the capital costs of pipes and tanks as well as the present value of the energy consumed during a specified period. Optimization tends to reduce costs by reducing the diameter of, or completely eliminating, some pipes, thus leaving the system with insufficient capacity to respond to pipe breaks or demands that exceed design values without violating required performance levels. A resilience index is considered as a second objective to increase the hydraulic reliability and availability of water during pipe failures. Sensitivity analysis of solutions on the payoff curve generated by twin-objective optimization shows poor performance of these networks under random pipe failure or a pump being out of service. The minimum surplus head is added as a third objective to overcome the shortcomings of the resilience index. Results are presented for the payoff characteristics between total cost and reliability for 24 h design and five loading conditions.