arXiv subjects

Anupam Saxena

Publications and source records attributed to Anupam Saxena.

15 recordsLinked to original sources

arXiv2026

A generalized shape function approach for multimaterial topology optimization

This paper presents a generalized shape function (gSF) approach for multi-material topology optimization that utilizes a compact design space to produce optimized configurations featuring a large number of materials. Building upon 1D (linear), 2D (bilinear), and 3D (trilinear) shape functions, generalized nD (n-linear) shape functions are conceptualized to map the multi-material simplex domain. Natural coordinates of these shape functions are considered the design variables used to determine the material densities. These densities are mathematically proven to satisfy the essential barycentric properties, guaranteeing a physically valid material interpolation space. Furthermore, we demonstrate that applying density filtering directly to the natural coordinates is mathematically equivalent to filtering the densities themselves, and that the tailored projection scheme preserves these vital barycentric properties in the projected states. The versatility, efficacy, and success of the gSF approach are demonstrated across various 2D and 3D stiff-structure (SS) and compliant-mechanism (CM) design problems. Strain energy is minimized for SS, whereas a multicriteria objective is minimized for CMs with given volume constraints. Sensitivity analysis is performed using the adjoint variable method, and the optimization problem is solved using the method of moving asymptotes. Results for SSs and CMs in 2D and 3D, respectively, up to 24 and 15 different materials, are presented. Objective history plots indicate smooth convergence. The proposed approach removes practical restrictions on the number of candidate materials, offering excellent scalability for large-scale engineering applications.

cs.CE↗

arXiv2025

Design optimization and robustness analysis of rigid-link flapping mechanisms

Rigid link flapping mechanisms remain the most practical choice for flapping wing micro-aerial vehicles (MAVs) to carry useful payloads and onboard batteries for free flight due to their long-term durability and reliability. However, MAVs with these mechanisms require significant weight reduction to achieve high agility and maneuverability. One approach involves using single-DOF planar rigid linkages, which are rarely optimized dimensionally for high lift and low power, considering their sweeping kinematics and the unsteady aerodynamic effects. We integrated a mechanism simulator based on a quasistatic nonlinear finite element method with an unsteady vortex lattice method-based aerodynamic analysis tool within an optimization routine. We optimized three different mechanism topologies from the literature. Significant power savings were observed up to 34% in some cases, due to increased amplitude and higher lift coefficients resulting from optimized asymmetric sweeping velocity profiles. We also conducted a robustness analysis to quantify performance sensitivity to manufacturing tolerances. It provided a trade-off between performance and reliability and revealed the need for tight manufacturing tolerances and careful material selection. Finally, the analysis helped select the best mechanism topology, as we observed significant variation in sensitivity to manufacturing tolerances and peak input torque values across different topologies for a given design lift value. The presented unified computational tool can find application in flapping mechanism topology optimization, as it can simulate any generic single-DOF planar rigid linkage without supplying kinematics manually.

cs.RO↗

arXiv2024

Normalized field product approach: A parameter-free density evaluation method for close-to-binary solutions in topology optimization with embedded length scale

This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid phase, allowing for smooth and transition-free topologies. The density evaluation does not rely on weight functions; however, the related density functions must have values between 0 and 1. The method combines the SIMP scheme and the introduced density function for material stiffness interpolation. The success and efficacy of the approach are demonstrated for designing both two- and three-dimensional designs, encompassing stiff structures and compliant mechanisms. The structure's compliance is minimized for the former, while the latter involves optimizing a multi-criteria objective. Numerical examples consider different volume fractions, length scales, and density functions. A volume-preserving smoothing and resolution scheme is implemented to achieve serrated-free boundaries. The proposed method is also seamlessly extended with advanced elements for solving 3D problems. The optimized designs obtained are close to binary without any user intervention while satisfying the desired feature size on the solid phase.

cs.CE↗

arXiv2024

Topology optimization of contact-aided compliant mechanisms for tracing multi-kink paths

This paper presents a topology optimization approach to design 2D contact-aided compliant mechanisms (CCMs) that can trace the desired output paths with more than one kink while experiencing self and/or external contacts. Such CCMs can be used as mechanical compliant switches. Hexagonal elements are used to parameterize the design domain. Negative circular masks are employed to remove material beneath them and generate rigid contact surfaces. Each mask is assigned five design variables. The first three decide the location and radius of the mask, whereas the last two determine the presence of the contact surface and its radius. To ensure continuity in contacting surfaces' normal, we employ a boundary smoothing scheme. The augmented Lagrange multiplier method is employed to incorporate self and mutual contact. An objective is formulated using the Fourier shape descriptors with the permitted resource constraint. The hill-climber optimization technique is utilized to update the design variables. An in-house code is developed for the entire process. To demonstrate the method's efficacy, a CCM is optimized with a two-kink path. The desired and obtained paths are compared.

cs.CE↗

arXiv2023

PyHexTop: a compact Python code for topology optimization using hexagonal elements

Python serves as an open-source and cost-effective alternative to the MATLAB programming language. This paper introduces a concise topology optimization Python code, named ``\texttt{PyHexTop}," primarily intended for educational purposes. Code employs hexagonal elements to parameterize design domains as such elements provide checkerboard-free optimized design naturally. \texttt{PyHexTop} is developed based on the ``\texttt{HoneyTop90}" MATLAB code~\cite{kumar2023honeytop90} and uses the \texttt{NumPy} and \texttt{SciPy} libraries. Code is straightforward and easily comprehensible, proving a helpful tool that can help people new in the topology optimization field to learn and explore. \texttt{PyHexTop} is specifically tailored to address compliance minimization with specified volume constraints. The paper provides a detailed explanation of the code for solving the Messerschmitt-Bolkow-Blohm beam and extensions to solve problems different problems. The code is publicly shared at: https://github.com/PrabhatIn/PyHexTop

cs.CE↗

arXiv2022

An improved Material Mask Overlay Strategy for the desired discreteness of pressure-loaded optimized topologies

This paper presents a Material Mask Overlay topology optimization approach with the improved material assignment at the element level for achieving the desired discreteness of the optimized designs for pressure-loaded problems. Hexagonal elements are employed to parametrize the design domain. Such elements provide nonsingular local connectivity; thus, checkerboard patterns and point connections inherently get subdued. Elliptical negative masks are used to find the optimized material layout. Each mask is represented via seven parameters that describe the location, shape, orientation, material dilation, and erosion variables of the mask. The latter two variables are systematically varied in conjunction with a grayscale measure constraint to achieve the solutions' sought 0-1 nature. Darcy's law with a drainage term is used to model the pressure load. The obtained pressure field is converted into the consistent nodal forces using Wachspress shape functions. Sensitivities of the objective and pressure load are evaluated using the adjoint-variable method. The efficacy and robustness of the approach are demonstrated by solving various pressure-loaded structures and pressure-driven compliant mechanisms. Compliance is minimized for loadbearing structures, whereas a multicriteria objective is minimized for mechanism designs. The boundary smoothing scheme is implemented within each optimization iteration to subdue the designs' undulated boundaries.

cs.CE↗

arXiv2022

Normalized Field Product method for Topology Optimization

The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity free solutions to exist within the design space. The density formulation proposed herein is independent of user specified parameters, other then the length scale. Sensitivity analysis for the formulation obtained by combining the proposed density evaluation with the SIMP material model reveal that for compliance minimization and small deformation compliant mechanism problems, objective gradients vanish at pure 0-1 topologies. The methodology is implemented to solve well known examples in literature for different mesh refinements presenting mesh independent and close to binary solutions without the use of heuristics or continuation methods.

math-ph↗

arXiv2022

Topology Optimization with Tetra-kai-decahedra and Spheroidal Masks

A novel meshing scheme, based on regular tetra-kai-decahedron, also referred to as truncated octahedron, cells is presented for use in spatial topology optimization. A tetra-kai-decahedron mesh ensures face connectivity between elements thereby eliminating singular solutions from the solution space. Various other benefits of implementing the said mesh are also highlighted, and the corresponding finite element is introduced. Material mask overlay strategy or MMOS, a feature based method for topology optimization is extended for use in 3-dimensions (MMOS-3D) via the aforementioned finite element and spheroidal negative masks. Formulation for density computation and sensitivity analysis for gradient based optimization is developed. Examples on traditional structural topology optimization problems are presented with detailed discussion on efficacy of the proposed approach.

cs.CE↗

arXiv2022

Compliant Constant Output/ Input Force Mechanisms- Topology Optimization with Contact

We synthesize monolithic topologies of constant output (CoFM) and input (CiFM) force mechanisms. During synthesis, we capture all possible aspects of member deformation including finite displacements, buckling, interaction between members, their interaction with external surfaces, and importantly, interaction of the mechanism with flexible workpieces to capture force transfer in true sense. Features of constant force characteristics, e.g., magnitude(s) of the desired force(s), range of input displacement over which slope of the force displacement curve is near zero, and distance between workpiece and the mechanism are controlled individually via novel objectives proposed herein. Two of the constant output and constant input force mechanisms each, are synthesized using stochastic optimization ensuring ready manufacturability. We observe that presence of external surfaces may not be required for singlepiece mechanisms to attain constant force characteristics. However, interesting solutions are possible if mutual contact is permitted. We also note that desired force characteristics may not remain the same with alteration in the workpieces shape and (or) material properties. We finally fabricate and test the synthesized mechanisms and find that the desired constant force characteristics are by and large retained.

cs.CE↗

arXiv2020

On topology optimization of large deformation contact-aided shape morphing compliant mechanisms

A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal elements. Negative circular masks are employed to perform dual task, i.e., to decide material states of each element and also, to generate rigid contact surfaces. Each mask is characterized by five design variables, which are mutated by a zero-order based hill-climbing optimizer. Geometric and material nonlinearities are considered. Continuity in normals to boundaries of the candidate designs is ensured using a boundary resolution and smoothing scheme. Nonlinear mechanical equilibrium equations are solved using the Newton-Raphson method. An updated Lagrange approach in association with segment-to-segment contact method is employed for the contact formulation. Both mutual and self contact modes are permitted. Efficacy of the approach is demonstrated by designing four contact-aided shape morphing compliant mechanisms for different desired curves. Performance of the deformed profiles is verified using a commercial software. The effect of frictional contact surface on the actual profile is also studied

cs.CE↗

arXiv2020

On Topology optimization with elliptical masks and honeycomb tessellation with explicit length scale constraints

Topology optimization using gradient search with negative and positive elliptical masks and honeycomb tessellation is presented. Through a novel skeletonization algorithm for topologies defined using filled and void hexagonal cells/elements, explicit minimum and maximum length scales are imposed on solid states in the solutions. An analytical example is presented which suggests that for a skeletonized topology, optimal solutions may not always exist for any specified volume fraction, minimum and maximum length scales, and that there may exist implicit interdependence between them. A Sequence for Length Scale (SLS) methodology is proposed wherein solutions are sought by specifying only the minimum and maximum length scales with volume fraction getting determined systematically. Through four benchmark problems in small deformation topology optimization, it is demonstrated that solutions by-and-large satisfy the length scale constraints though the latter may get violated at certain local sites. The proposed approach seems promising, noting especially that solutions, if rendered perfectly {\it black and white} with minimum length scale explicitly imposed and boundaries smoothened, are quite close in performance compared to the parent topologies. Attaining {\it volume distributed} topologies, wherein members are more or less of the same thickness, may also be possible with the proposed approach.

cs.CE↗

arXiv2020

Comprehending finger flexor tendon pulley system using a computational analysis

Existing prosthetic/orthotic designs are rarely based on kinetostatics of a biological finger, especially its tendon-pulley system (TPS) which helps render a set of extraordinary functionalities. Studies on computational models or cadaver experiments do exist. However, they provide little information on TPS configurations that lead to lower tendon tension, bowstringing, and pulley stresses, all of which a biological finger may be employing after all. A priori knowledge of such configurations and associated trade-offs is helpful not only from the design viewpoint of, say, an exoskeleton but also for surgical reconstruction procedures. We present a parametric study to determine optimal TPS configurations for the flexor mechanism. A compliant, flexure-based computational model is developed and simulated using the pseudo rigid body method, with various combinations of pulley/tendon attachment point locations, pulley heights, and widths. Deductions are drawn from the data collected to recommend the most suitable configuration. Many aspects of the biological TPS configuration are explained through the presented analysis. We reckon that the analytical approach herein will be useful in arriving at customized (optimized) hand exoskeletal designs.

cs.RO↗

arXiv2020

Topology synthesis of a 3-kink contact-aided compliant switch

A topology synthesis approach to design 2D Contact-aided Compliant Mechanisms (CCMs) to trace output paths with three or more kinks is presented. Synthesis process uses three different types of external, rigid contact surfaces: circular, elliptical and rectangular: which in combination, offer intricate local curvatures that CCMs can benefit from, to deliver desired, complex output characteristics. A network of line elements is employed to generate topologies. A set of circular subregions is laid over this network, and external contact surfaces are generated within each subregion. Both, discrete and continuous design variables are employed: the former set controls the CCM topology, appearance and type of external contact surfaces, whereas the latter set governs shapes and sizes of the CCM constituents, and sizes of contact surfaces. All contact types are permitted with contact modeling made significantly easier through identification of outer and inner loops. Line topologies are fleshed out via a user-defined number of quadrilateral elements along lateral and longitudinal directions. Candidate CCM designs are carefully preprocessed before analysis via a commercial software and evolution using a stochastic search. The process is exemplified via a contact-aided, 3-kink mechanical switch which is thoroughly analysed in presence of friction and wear.

cs.CE↗

arXiv2018

Computational synthesis of large deformation compliant mechanisms undergoing self and mutual contact

Topologies of large deformation Contact-aided Compliant Mechanisms (CCMs), with self and mutual contact, exemplified via path generation applications, are designed using the continuum synthesis approach. Design domains are parameterized using honeycomb tessellation. Assignment of material to each cell, and generation of rigid contact surfaces, are accomplished via suitably sizing and positioning negative circular masks. To facilitate contact analysis, boundary smoothing is implemented. Mean value coordinates are employed to compute shape functions, as many regular hexagonal cells get degenerated into irregular, concave polygons as a consequence of boundary smoothing. Both, geometric and material nonlinearities are considered in the finite element analysis. The augmented Lagrange multiplier method in association with an active set strategy is employed to incorporate both self and mutual contact. CCMs are evolved using the stochastic hill climber search. Synthesized contact-aided compliant continua trace paths with single and importantly, multiple kinks and experience multiple contact interactions pertaining to both self and mutual contact modes.

cs.CE↗

arXiv2018

ABC Conjecture: $ABC = 2^m p^n q^r$ with Fermat or Mersenne Primes

For $p$ and $q$ any two distinct Fermat or Mersenne primes, $m,n,r$ as positive integers and $\mu = \pm 1$ satisfying any diophantine relation, $\mbox{(i)}\; 2^m + \mu = p^nq^r, \mbox{(ii)} \; 2^mp^n + \mu = q^r \mbox{ or } \mbox{(iii)} \; p^n + \mu q^r = 2^m$, it is shown that the number of triplets $\{A, B, C \}$ with $\gcd(A,B) = 1$ and $C = A + B$, for which their product is of the form $ABC = 2^mp^nq^r$ and which satisfy $C > \mathrm{rad}(ABC)^{1 + \varepsilon}$ for any real $\varepsilon > 0$, is finite. For the triplet $\{2^{y+1}, 2^{2y}+1, (2^y+1)^2\}$, a solution to (iii) with positive integer $y$ such that $2^y+1$ and $2^{2y}+1$ are primes, $\mathrm{rad}(ABC)^{1 + \varepsilon} > C$ holds for any $\varepsilon > 0$. Furthermore, finiteness of the number of solutions of (iii) when $n$ is even, is demonstrated elsewhere (Ref. [64]). All other solutions are enumerated.

math.NT↗