A numerical method of lower bound dynamic shakedown analysis for 3D structures

PurposeThe safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.Design/methodology/approachThe construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.FindingsThree-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.Research limitations/implicationsIn this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.Originality/valueThis study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

On the stress dependence of the elastic tensor

Summary The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the equilibrium deformation gradient relative to a fixed choice of reference body. Inversion of the relation between the deformation gradient and stress might, therefore, be expected to lead neatly to the desired expression for the elastic tensor. Unfortunately, the deformation gradient can only be recovered from the stress up to a choice of rotation matrix. Hence it is not possible in general to express the elastic tensor as a unique function of the equilibrium stress. By considering material symmetries, though, it is shown that the degree of non-uniqueness can sometimes be reduced, and in some cases even removed entirely. These results are illustrated through a range numerical calculations, and we also obtain linearised relations applicable to small perturbations in equilibrium stress. Finally, we make a comparison with previous studies before considering implications for geophysical forward- and inverse-modelling.

Elastic Coefficients of β-HMX as Functions of Pressure and Temperature from Molecular Dynamics

The isothermal second-order elastic stiffness tensor and isotropic moduli of β-1,3,5,7- tetranitro-1,3,5,7-tetrazoctane (β-HMX) were calculated, using the P21/n space group convention, from molecular dynamics for hydrostatic pressures ranging from 10−4 to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite strains on the equilibrated β-HMX crystal at a given pressure and temperature and using the equilibrium stress tensors of the strained cells to obtain the derivatives of stress with respect to strain. For a fixed temperature, the elastic coefficients increase substantially with increasing pressure, whereas, for a fixed pressure, the elastic coefficients decrease as temperature increases, in accordance with physical expectations. Comparisons to previous experimental and computational results are provided where possible.

The Anelastic Ericksen Problem: Universal Deformations and Universal Eigenstrains in Incompressible Nonlinear Anelasticity

Ericksen’s problem consists of determining all equilibrium deformations that can be sustained solely by the application of boundary tractions for an arbitrary incompressible isotropic hyperelastic material whose stress-free configuration is geometrically flat. We generalize this by first, using a geometric formulation of this problem to show that all the known universal solutions are symmetric with respect to Lie subgroups of the special Euclidean group. Second, we extend this problem to its anelastic version, where the stress-free configuration of the body is a Riemannian manifold. Physically, this situation corresponds to the case where nontrivial finite eigenstrains are present. We characterize explicitly the universal eigenstrains that share the symmetries present in the classical problem, and show that in the presence of eigenstrains, the six known classical families of universal solutions merge into three distinct anelastic families, distinguished by their particular symmetry group. Some generic solutions of these families correspond to well-known cases of anelastic eigenstrains. Additionally, we show that some of these families possess a branch of anomalous solutions, and demonstrate the unique features of these solutions and the equilibrium stress they generate.

Long Working Hours, Stress, Turnover and Organization Commitment among Employees in Banking Sector

The main aim of the study is to examine the impact of a long working hour on stress, turnover and commitment of employees in the baking sector District Swabi. Stress affects the state of equilibrium. Stress is the reaction on the employees when there are a lot of pressures on them it can be workload, office environment or other factors. The data were collected through self-administrated from 234 respondents of the banking sector. The findings of the study show that there is a positive relationship between long working hours with turnover and stress while a negative relationship with organizational commitment. For enhancing both organizational and employee's productivity, the administration and policymakers need to increase compensations, organizational commitment and rewards. This study also provides the limitations and recommendations for further research.

Form-Finding of Spine Inspired Biotensegrity Model

This paper presents a study on form-finding of four-stage class one self-equilibrated spine biotensegrity models. Advantageous features such as slenderness and natural curvature of the human spine, as well as the stabilizing network that consists of the spinal column and muscles, were modeled and incorporated in the mathematical formulation of the spine biotensegrity models. Form-finding analysis, which involved determination of independent self-equilibrium stress modes using generalized inverse and their linear combination, was carried out. Form-finding strategy for searching the self-equilibrated models was studied through two approaches: application of various combinations of (1) twist angles and (2) nodal coordinates. A total of three configurations of the spine biotensegrity models with different sizes of triangular cell were successfully established for the first time in this study. All members in the spine biotensegrity models satisfied the assumption of linear elastic material behavior. With the established spine biotensegrity model, the advantageous characteristics of flexibility and versatility of movement can be further studied for potential application in deployable structures and flexible arm in the robotic industry.

An observation of the evolution of equilibrium stress on poly(lactic acid) and poly(lactic acid)/hydroxyapatite nanocomposites

Relaxation behavior provides specific information that indicates stress development with elapsed time for the determination of material characterization and constituting of material modeling. In addition, anomalous relaxation behavior of polymeric materials enables experimental analysis of some theoretical variables in constitutive equation. Equilibrium stress is one of the most prevailing variables in material modeling and it is generally considered as unmeasurable. In this study, evolution of equilibrium stress was examined with relaxation tests of two semi crystalline polymer materials, one of which was found to reach precise equilibrium stress levels. In accordance with this purpose, extensive relaxation tests were conducted on poly(lactic acid) and poly(lactic acid)/hydroxyapatite nanocomposites specimens at a wide range of temperatures from 23 ℃ and 55 ℃, and stress levels from 1 MPa to 50 MPa for poly(lactic acid) and 51 MPa for poly(lactic acid)/hydroxyapatite nanocomposites. All the specimens were subjected tensile loading–unloading and partial retraction process. The starting points of the relaxation test were chosen on unloading segment of stress–strain curves. Evolution of stress may decay, increase or decay then increase depending on the test point on unloading curves. Relaxation behavior of poly(lactic acid) and poly(lactic acid)/hydroxyapatite nanocomposites was simulated using viscoplasticity theory based on overstress for polymeric materials. Experimental results of poly(lactic acid) and poly(lactic acid)/hydroxyapatite nanocomposites were matched with numerical results of viscoplasticity theory based on overstress for polymeric materials, and viscoplasticity theory based on overstress for polymeric material model was found to have an aptitude for predicting anomalous relaxation behavior of poly(lactic acid) and poly(lactic acid)/hydroxyapatite nanocomposites. Additionally, the effect of temperature on relaxation time was investigated with using Kohlraush–Williams–Watts time-decay function. Modeling capability of Kohlrausch–Williams–Watts model was reasonable to predict short-term simple relaxation of poly(lactic acid) and poly(lactic acid)/hydroxyapatite nanocomposites. Responses of the model showed that interaction between relaxation time and environmental temperature was related to transition from glass state to rubbery state.

Texture and rheological evaluation of aerated confectionery

Confectionery industry represents a field that uses a large number of ingredients and techniques to develop unique sweet products. To produce aerated confectionery samples two different procedures were used to incorporate the ingredients in the beating vegetable or dairy cream. The objective of this research was to determine the texture parameters and the viscoelastic properties of aerated confections using compression stress-relaxation test and applying a modified Maxwell model. The highest fat content was presented by dairy cream aerated samples (20.04-20.25%), while the samples based on vegetable cream displayed a lower fat content. By applying the modified Maxwell mechanical model to the relaxation curves the equilibrium stress, σe, relaxation time, λrel, viscosity, η, and modulus of elasticity, G0, were determined. The aerated samples’ viscosity was greater than 137.96 kPa·s and less than 451.793 kPa·s; furthermore, Pearson correlation showed that density influences positively this rheological parameter (r = 0.955*). Fixing air into the product structure causes a decrease in density (0.388-0.788 g/cm3), leading to a lower equilibrium stress, a lower elasticity modulus and also a decrease of viscosity and relaxation time.

Multicultural Stress Management

Stress is a specific response by the body to a stimulus which tends to disturb the normal physiological equilibrium. Stress management skill can be culturally different due to the different parenting styles that is more popular in a culture. Diet is also related to stress as the mind and body are interrelated. Some evidences shown that staple diet had given rise to Parkinson or Alzheimer. Thus, nutrition and psychotherapy need to go together for effective stress management. Much evidence has supported the use of Ketogenic diet to manage stress. Psychotherapy, particularly schema therapy could manage stress through focusing on creating disassociation between our own vulnerability and our internalized critical voice. US recently focused on balancing imbalanced neurotransmitters in reducing stress symptoms. Lab tests can help detect the levels of our neurotransmitters and identify any imbalance of individual neurotransmitters contributing to stress related disorders, which are now available in Malaysia.

Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls

Rolling back-up rolls require high fracture toughness, particularly in the shaft portion, and high-hardness in the sleeve portion. The rolls are classified into two types; one is an integrated type and the other is a shrink-fitted type consisting of a sleeve and a shaft. The shrink-fitted roll has several advantages, for example, suitable materials can be chosen and the shaft can be reused by replacing the damaged sleeve. However, during use if the residual permanent deflection occurs, the roll cannot be used anymore. In this paper, an elastic-contact finite element method FEM analysis is performed to explain the residual permanent deflection mechanism. It is found that the quasi-equilibrium stress zone with the residual displacement causes the permanent slippage in the axial direction. In a similar way, the interface creep in the circumferential direction can be also explained from the quasi-equilibrium stress zone with the residual displacement.