Lightweight design and topology optimization of marine structures using peridynamics

Reducing the structural weight of the engineering parts is one of the key concerns for various manufacturing fields such as marine, aerospace, and automotive industries. Topology optimization would be a promising tool to design lighter and more cost-effective marine structures. In this paper, we utilize peridynamics- based topology optimization procedure for reducing the weight of marine structures. The objective function of the optimization problem here is compliance (i.e., total strain energy) where the constraint is defined as a target volume. Peridynamics is a non-local formulation of classical continuum mechanics and has superior advantages as compared to the finite element method in modeling structural discontinuities. For this reason, possible cracks or damages are also included in the initial design domain to avoid failures during the operation period of these marine structures. The results show superior design and optimum topology of a bulkhead for applications to relevant ships

Enhanced ship cross-section design methodology using peridynamics topology optimization

In this study, peridynamics topology optimization (PD-TO) framework is implemented to reduce the total weight of ship structures and increase their structural endurance against cracks. PD-TO is a general nonlocal optimization strategy that performs the minimization of strain energy density as the objective function and uses pre-defined volume fractions as optimization constraints. To analyze ship structures herein, both the optimality criteria (OC) algorithm and the proportional (PROP) approach are implemented into the PD-TO solver. As the initial design domain, a reference bulkhead geometry of trailing suction hopper dredger (ship) is modeled. This web frame is optimized according to critical wave/loading conditions such as hogging and sagging. Different volume fractions are investigated to obtain lighter designs based on OC and PROP methods. In addition, different cracked scenarios are created by locating the cracks into various positions on the reference ship cross-section. Optimized results for cracked cases shows that the proposed method can create alternative web frames for specific definitions of the possible damaged regions on the board. To prove the efficiency of the proposed method, maximum displacements and compliance of the reference and optimized structures are compared. The results proves that topologically optimized designs offered stiffer structures as compared to conventional designs under the same loading conditions. Finally, some of the optimized results are smoothed to demonstrate the practical utility of the PD-TO for manufacturing. Overall, it is revealed that the PD-TO can be effectively utilized to design marine structures to achieve a higher strength/weight ratio while considering critical operation conditions and possible damaged regions

Particle inverse method for full-field displacement and crack propagation monitoring from discrete sensor measurements

This study presents the Particle Inverse Method (PIM), a novel structural health monitoring technique for real-time, full-field monitoring of deformations and damages/cracks in structures using discrete sensor data. Towards this end, the PIM mathematically unifies the concepts of the inverse finite element method and peridynamics differential operator for the first time, thus creating a fully meshless approach that relies solely on particle discretization of the physical domain to solve the inverse problem of shape sensing. Utilizing a least squares variational principle, the PIM matches experimental measurements with numerical strains derived through interactions among particles in a non-local framework. This innovative principle allows the reconstruction of continuous deformations in the physical domain (for every particle) from discrete strain data. Additionally, the PIM uses a local damage parameter for each particle, dependent on the integrity of its bonds, to monitor crack development and propagation in real time. Crucially, PIM does not require information about loading or material properties for effective shape sensing and structural health monitoring. The method is applicable even if the crack continues to propagate in the physical domain. The accuracy of PIM is validated through comparative numerical analyses on benchmark problems involving both intact and cracked isotropic plates under tension and shear. Despite the limited number of sensors, PIM demonstrates its ability to accurately map full-field deformations and monitor crack dynamics effectively, highlighting its significant potential for future experimental applications

Coupling of bond-based peridynamics and continuous density-based topology optimization methods for effective design of three-dimensional structures with discontinuities

This study proposes continuous density-based three-dimensional topology optimization (TO) approaches developed by coupling the peridynamic theory (PD) with optimality criteria (OC) and proportional approach (PROP). These frameworks, abbreviated as PD-OC-TO and PD-PROP-TO, can be practically utilized to enhance the fracture toughness of the structures during the optimization process by taking critical regions into account as pre-defined cracks. Breaking the non-local interactions (bonds) between relevant PD particles enables us to readily model cracks. Utilizing this advantage, we solve several benchmark optimization problems including different numbers, positions, and alignments of the cracks. The major differences between the proposed methods are examined by comparing optimum topologies for various cracked scenarios. Moreover, the mechanical behaviour of the optimized structures is investigated under dynamic loads to prove the significant improvements achieved by the present approach in the final designs. The results of dynamic analyses reveal the viability of both PD-TO methods for increasing the fracture toughness of the structure in the optimization stage. Overall, the proposed approach is confirmed as a superior design and optimization tool for future engineering structures. Graphical abstract: (Figure presented.

Peridynamics-informed effect of micro-cracks on topology optimization of lightweight structures

Most structures are preferred to be light-weighted when they are used in industrial applications such as automotive, aerospace, and naval structures. Classical continuum mechanics (CCM) formulations are commonly adopted to solve the topology optimization problems. However, CCM brings about some restrictions to the modeling, analysis, and solution of complex structures with structural discontinuities, defects, and micro/macro damages. Unlike CCM, peridynamic theory provides a wider range of analysis options because of its nonlocal integration nature, which can eliminate the need for partial derivatives in the equation of motion, thereby being suitable for effective modeling of cracks, damages, etc. This paper presents an application of peridynamics based topology optimization (PD-TO) to study the effect of micro-damages for designing lightweight engineering structures. The PD-TO algorithm used herein is based on the coupling of bond-based method and Optimality Criteria (OC) topology optimization method. The structure is designed by locating various microcracks for investigating the microdamage effect on the optimal topologies. To this end, the PD-TO model is implemented using an in-house MATLAB code, and strain energy density distributions are compared between different topologies. As a result, the importance of including damage regions within the lightweight design optimization stage is revealed

Peridynamics topology optimization of three-dimensional structures with surface cracks for additive manufacturing

Additive manufacturing (AM) is an effective approach to fabricating intricate shapes obtained from topology optimization (TO). However, it may cause undesired manufacturing-induced defects/cracks due to high thermal residual stresses. This study proposes a PeriDynamics-enabled three-dimensional Topology Optimization method (PD-TO) for designing structures by considering surface cracks for the AM processes. The PD-TO approach employs a bi-directional evolutionary structural optimization method and uses particle discretization of geometry for mechanical analysis. Crack surfaces are generated by breaking three-dimensional nonlocal interactions of the particles, and thus, during the optimization process, complex multiple structural discontinuities can be diligently modeled. First, the proposed approach is validated by solving benchmark problems without cracks. For each benchmark geometry, the PD-TO analysis is then performed by considering different positions and numbers (single/multiple) of cracks. These analyses extensively investigate and demonstrate the effects of a priori knowledge of residual stress-induced damages/cracks on the optimum topology for additive manufacturing. Besides, the smoothing operation is applied to the optimum designs to transform voxel shapes into AM-friendly smooth surfaces. These geometries are manufactured by an extrusion-based AM process to demonstrate the practical engineering application of the proposed method. Finally, the comparison of numerical results is also supported by the experimental tests conducted on the optimized topologies. Overall, it is confirmed that the PD-TO approach is a viable and accurate optimization tool for additive manufacturing considering possible process-induced damages

Combination of peridynamics and genetic algorithm based topology optimization methods for additive manufacturing-friendly designs

Topology optimization (TO) is a practical tool to generate light-weighted engineering structures for various manufacturing industries. However, manufacturing constraints and surface smoothing are still considerable challenges for TO algorithms. Existing TOframeworks utilize mechanical analysis approaches that discretize the whole domain with elements or particles. Therefore, obtained geometries from TO have been criticized for their complex shapes. In this study, we propose a coupled framework to generate additive manufacturing (AM)-friendly designs which result in less support structure and higher surface quality. For this purpose, the generative topology optimization method (GTO), which uses genetic algorithm to search for the best alternative set of geometry within all the possible topology results, is coupled with the peridynamics topology optimization (PD-TO) method to evolve the PD-TO results into AM-friendly shapes. The PD-TO discretizes the problem domain using equally spaced particles during the TO process. Hence, PD-TO generates a point cloud file with relevant artificial material density values in the final state. Then, the GTO method utilizes the point cloud and material densities as an input file to achieve better final geometry. AM-friendly designs achieved from GTO are compared with the initial results obtained from PD-TO to demonstrate the efficiency and capability of the proposed method