Search for: All records

Fatigue analysis in metallic frame structures can be challenging due to associated computational costs; if localized plasticity is involved, then the approach of three-dimensional (3D) continuum plasticity models for direct computation of stresses will be infeasible for the analysis of cyclic loading that would need to be modeled in medium- to high-cycle fatigue and vibratory fatigue applications. This difficulty is particularly accentuated in architected structures, for which high-resolution 3D finite element analysis (FEA) would be prohibitively expensive. In this work, we propose an alternative approach based on the use of novel elasto-plastic frame model with continuous flow (i.e. no sharp yield function) for modeling 3D frame and lattice structures. Rather than splitting the strains (as is done in classical plasticity) we split the deformation measures, extension, curvature and twist, into elastic and plastic components and postulate a rate type evolution rule for the plastic variables in terms of the stress resultants (axial force, bending moment, and torque). The combination of structural models together with the use of elasto-plastic operator split to solve the resulting boundary value problem allows for much faster determination of localized plasticity than continuum models can provide. The use of a continuous transition from elastic to rate-independent plasticity (as opposed to an abrupt change with classical plasticity models) allows us to capture localized microplasticity and determine resulting fatigue progression using a cycle-count-free, plastic work-based approach, formulated in terms of the curvatures and resultants. We demonstrate that (a) the model is able able to reproduce the response of 3D FEA with very few elements and (b) the model has the ability to rapidly predict the fatigue life under variable amplitude combined loading with relatively few frame elements. 

It has been well established that the internal length scale related to the cell size plays a critical role in the response of architected structures. It this paper, a Volterra derivative-based approach for deriving nonlocal continuum laws directly from an energy expression without involving spatial derivatives of the displacement is proposed. A major aspect of the work is the introduction of a nonlocal derivative-free directionality term, which recovers the classical deformation gradient in the infinitesimal limit. The proposed directionality term avoids issues with correspondences under nonsymmetric conditions (such a unequal distribution of points that cause trouble with conventional correspondence-based approaches in peridynamics). Using this approach, we derive a nonlocal version of a shear deformable beam model in the form of integro-differential equations. As an application, buckling analysis of architected beams with different core shapes is performed. In this context, we also provide a physical basis for the consideration of energy for nonaffine (local bending) deformation. This removes the need for additional energy in an ad hoc manner towards suppressing zero-energy modes. The numerical results demonstrate that the proposed framework can accurately estimate the critical buckling load for a beam in comparison to 3-D simulations at a small fraction of the cost and computational time. Efficacy of the framework is demonstrated by analysing the responses of a deformable beam under different loads and boundary conditions. 

The internal length scale relating to the cell size plays a crucial role in predicting the response of architected structures when subjected to external stimuli. A Volterra derivative-based approach for arriving at the non-local derivative-free continuum laws for architected structures is proposed. A mainstay of the work is the derivative-free directionality term, which recovers its classical counterpart in the infinitesimal limit. Using this approach, we derive the non-local integro-differential governing equations of a shear deformable plate. We also suggest a physical basis for the consideration of energy for nonaffine deformations and accurately estimate it by performing buckling analysis. This discards the requirement of the additional energy to be incorporated in an arbitrary manner for suppressing the unwanted spurious oscillations induced from zero energy modes. The numerical results demonstrate the efficacy of the proposed framework in precisely capturing the mechanical response of web-core shear deformable plate, thereby, manifesting the supremacy of the reduced model in shrinking the cost and computational time. To bolster our claim, various numerical models with different loading conditions have been analysed and compared against the three-dimensional FEM results. 

Abstract An automatic complex topology lightweight structure generation method (ACTLSGM) is presented to automatically generate 3D models of lightweight truss structures with a boundary surface of any shape. The core idea of the ACTLSGM is to use the PIMesh, a mesh generation algorithm developed by the authors, to generate node distributions inside the object representing the boundary surface of the target complex topology structures; raw lightweight truss structures are then generated based on the node distributions; the resulting lightweight truss structure is then created by adjusting the radius of the raw truss structures using an optimization algorithm based on finite element truss analysis. The finite element analysis-based optimization algorithm can ensure that the resulting structures satisfy the design requirements on stress distributions or stiffness. Three demos, including a lightweight structure for a cantilever beam, a femur bone scaffold, and a 3D shoe sole model with adaptive stiffness, can be used to adjust foot pressure distributions for patients with diabetic foot problems and are generated to demonstrate the performance of the ACTLSGM. The ACTLSGM is not limited to generating 3D models of medical devices, but can be applied in many other fields, including 3D printing infills and other fields where customized lightweight structures are required.