# New parameterized solution with application to bounding secondary variables in finite element models of structures

## TL;DR

This paper introduces a novel parameterized outer estimate for the solution set of interval parametric linear systems, enhancing bounds in finite element models of structures with improved accuracy and applicability.

## Contribution

It presents a new parameterized solution method that offers advantages over existing approaches, enabling sharper bounds for derived quantities in structural finite element analysis.

## Key findings

- Demonstrates improved bounds for forces and stresses in finite element models.
- Provides numerical examples validating the effectiveness of the new method.
- Introduces a new approach for bounding secondary variables in structural analysis.

## Abstract

In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions considered so far. Some properties of the new parameterized solution, compared to the parameterized solution considered so far, and a new application direction are presented and demonstrated by numerical examples. The new parameterized solution is a basis of a new approach for obtaining sharp bounds for derived quantities (e.g., forces or stresses) which are functions of the displacements (primary variables) in interval finite element models of mechanical structures.